This module calculates the derivatives (gradients, Laplacians, etc.) of a function. More...

Detailed Description

This module calculates the derivatives (gradients, Laplacians, etc.) of a function.

Note: the function whose derivative is to be calculated has to be defined (1:mesh%np_part), while the (1:mesh%np) values of the derivative are calculated.

Data Types
type	derivatives_handle_batch_t
	handle to transfer data from the start() to finish() calls. More...

type	derivatives_t
	class representing derivatives More...

Functions/Subroutines
subroutine, public	derivatives_init (der, namespace, space, coord_system, order)

subroutine, public	derivatives_end (der)

subroutine	derivatives_get_stencil_lapl (der, lapl, space, coord_system, name, order)

subroutine, public	derivatives_lapl_diag (der, lapl)
	Returns the diagonal elements of the Laplacian, needed for preconditioning. More...

subroutine	derivatives_get_stencil_grad (der)

subroutine, public	derivatives_build (der, namespace, space, mesh, qvector, regenerate, verbose)
	build the derivatives object: More...

subroutine	stencil_pol_grad (stencil_type, dim, direction, order, polynomials)

subroutine	stencil_pol_lapl (stencil_type, stencil, dim, order, polynomials)

subroutine	get_rhs_lapl (coord_system, polynomials, chi, rhs, stencil_primitive_coordinates)

subroutine	get_rhs_grad (polynomials, dir, rhs)

subroutine	derivatives_make_discretization (namespace, der, nderiv, ideriv, op, name, verbose, order)

logical function	derivatives_overlap (this)

subroutine, public	derivatives_get_lapl (this, namespace, op, space, name, order)

logical function, dimension(1:this%mesh%np), public	derivatives_get_inner_boundary_mask (this)
	This function tells whether a point in the grid is contained in a layer of the width of the stencil between the last row of points in the grid. More...

real(real64) function, public	derivatives_lapl_get_max_eigenvalue (this)
	Get maximum eigenvalue of discrete Laplacian. For the star and star_general stencils, use the Fourier transform of the stencil evaluated at the maximum phase to get an upper bound on the spectrum. For all other stencils, use the upper bound from the continuum. More...

subroutine, public	dderivatives_perform (op, der, ff, op_ff, ghost_update, set_bc, factor)
	apply a nl_operator to a mesh function More...

subroutine, public	dderivatives_lapl (der, ff, op_ff, ghost_update, set_bc, factor)
	apply the Laplacian to a mesh function More...

subroutine, public	dderivatives_grad (der, ff, op_ff, ghost_update, set_bc, to_cartesian)
	apply the gradient to a mesh function More...

subroutine, public	dderivatives_partial (der, ff, op_ff, dir, ghost_update, set_bc)
	apply the partial derivative along dir to a mesh function More...

subroutine, public	dderivatives_div (der, ff, op_ff, ghost_update, set_bc, to_cartesian)
	apply the divergence operator to a vector of mesh functions More...

subroutine, public	dderivatives_curl (der, ff, op_ff, ghost_update, set_bc)
	apply the curl operator to a vector of mesh functions More...

subroutine, public	dderivatives_test (this, namespace, repetitions, min_blocksize, max_blocksize)
	unit test for derivatives More...

subroutine, public	dderivatives_batch_start (op, der, ff, opff, handle, ghost_update, set_bc, factor)
	apply a non-local operator to a batch (1st part) More...

subroutine, public	dderivatives_batch_finish (handle, async)
	apply a non-local operator to a batch (2nd part) More...

subroutine, public	dderivatives_batch_perform (op, der, ff, opff, ghost_update, set_bc, factor, async)
	apply an operator to a bach of mesh functions More...

subroutine, public	dderivatives_batch_grad (der, ffb, opffb, ghost_update, set_bc, to_cartesian, factor)
	apply the gradient to a batch of mesh functions More...

subroutine	dbatch_covector_to_cartesian (der, coord_system, uvw, xyz)
	transform a vector of batches from affine to cartesian coordinates More...

subroutine, public	dderivatives_batch_curl (der, ffb, ghost_update, set_bc)
	apply the curl to a batch of mesh functions More...

subroutine, public	dderivatives_batch_curl_from_gradient (der, ffb, gradb)
	calculate the curl from a batch and its gradient More...

subroutine, public	dderivatives_batch_div (der, ffb, opffb, ghost_update, set_bc, to_cartesian)
	calculate the divergence of a vector of batches More...

subroutine, public	zderivatives_perform (op, der, ff, op_ff, ghost_update, set_bc, factor)
	apply a nl_operator to a mesh function More...

subroutine, public	zderivatives_lapl (der, ff, op_ff, ghost_update, set_bc, factor)
	apply the Laplacian to a mesh function More...

subroutine, public	zderivatives_grad (der, ff, op_ff, ghost_update, set_bc, to_cartesian)
	apply the gradient to a mesh function More...

subroutine, public	zderivatives_partial (der, ff, op_ff, dir, ghost_update, set_bc)
	apply the partial derivative along dir to a mesh function More...

subroutine, public	zderivatives_div (der, ff, op_ff, ghost_update, set_bc, to_cartesian)
	apply the divergence operator to a vector of mesh functions More...

subroutine, public	zderivatives_curl (der, ff, op_ff, ghost_update, set_bc)
	apply the curl operator to a vector of mesh functions More...

subroutine, public	zderivatives_test (this, namespace, repetitions, min_blocksize, max_blocksize)
	unit test for derivatives More...

subroutine, public	zderivatives_batch_start (op, der, ff, opff, handle, ghost_update, set_bc, factor)
	apply a non-local operator to a batch (1st part) More...

subroutine, public	zderivatives_batch_finish (handle, async)
	apply a non-local operator to a batch (2nd part) More...

subroutine, public	zderivatives_batch_perform (op, der, ff, opff, ghost_update, set_bc, factor, async)
	apply an operator to a bach of mesh functions More...

subroutine, public	zderivatives_batch_grad (der, ffb, opffb, ghost_update, set_bc, to_cartesian, factor)
	apply the gradient to a batch of mesh functions More...

subroutine	zbatch_covector_to_cartesian (der, coord_system, uvw, xyz)
	transform a vector of batches from affine to cartesian coordinates More...

subroutine, public	zderivatives_batch_curl (der, ffb, ghost_update, set_bc)
	apply the curl to a batch of mesh functions More...

subroutine, public	zderivatives_batch_curl_from_gradient (der, ffb, gradb)
	calculate the curl from a batch and its gradient More...

subroutine, public	zderivatives_batch_div (der, ffb, opffb, ghost_update, set_bc, to_cartesian)
	calculate the divergence of a vector of batches More...

Variables
integer, parameter	der_bc_zero_f = 0
	function is zero at the boundaries More...

integer, parameter	der_bc_zero_df = 1
	first derivative of the function is zero More...

integer, parameter	der_bc_period = 2
	boundary is periodic More...

integer, parameter, public	der_star = 1

integer, parameter, public	der_variational = 2

integer, parameter, public	der_cube = 3

integer, parameter, public	der_starplus = 4

integer, parameter, public	der_stargeneral = 5

integer, parameter	blocking = 1

integer, parameter	non_blocking = 2

type(accel_kernel_t)	kernel_uvw_xyz

type(accel_kernel_t)	kernel_dcurl

type(accel_kernel_t)	kernel_zcurl

Function/Subroutine Documentation

◆ derivatives_init()

subroutine, public derivatives_oct_m::derivatives_init	(	type(derivatives_t), intent(inout), target	der,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		class(coordinate_system_t), intent(in)	coord_system,
		integer, intent(in), optional	order
	)

Definition at line 281 of file derivatives.F90.

◆ derivatives_end()

subroutine, public derivatives_oct_m::derivatives_end ( type(derivatives_t), intent(inout) der )

Definition at line 454 of file derivatives.F90.

◆ derivatives_get_stencil_lapl()

subroutine derivatives_oct_m::derivatives_get_stencil_lapl	(	type(derivatives_t), intent(in)	der,
		type(nl_operator_t), intent(inout)	lapl,
		class(space_t), intent(in)	space,
		class(coordinate_system_t), intent(in)	coord_system,
		character(len=80), intent(in), optional	name,
		integer, intent(in), optional	order
	)

private

Definition at line 486 of file derivatives.F90.

◆ derivatives_lapl_diag()

subroutine, public derivatives_oct_m::derivatives_lapl_diag	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(out)	lapl
	)

Returns the diagonal elements of the Laplacian, needed for preconditioning.

Parameters

[out] lapl lapl(meshnp)

Definition at line 524 of file derivatives.F90.

◆ derivatives_get_stencil_grad()

subroutine derivatives_oct_m::derivatives_get_stencil_grad ( type(derivatives_t), intent(inout) der )

private

Definition at line 541 of file derivatives.F90.

◆ derivatives_build()

subroutine, public derivatives_oct_m::derivatives_build	(	type(derivatives_t), intent(inout)	der,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		class(mesh_t), intent(in), target	mesh,
		real(real64), dimension(:), intent(in), optional	qvector,
		logical, intent(in), optional	regenerate,
		logical, intent(in), optional	verbose
	)

build the derivatives object:

This routine initializes the boundary conditions and builds the actual nl_operator_oct_m::nl_operator_t objects for the derivative operators.

The stencil weights are computed by imposing that the action of the discrete Laplacian or gradient is exact on a set of polynomials. The set of polynomials needs to be chosen such that it yields linearly independent vectors when evaluated on the points of the stencil.

More specifically, the weights are the solution of the equation

\[ mat * weights = rhs, \]

where \( mat_{i,j} \) is the value of the \(i\)-th polynomial on the \(j\)-the point of the stencil and \(rhs\) is the solution of applying the operator to the polynomial and evaluating it at 0.

The polynomials can be either computed in primitive or Cartesian coordinates and correspondingly the right-hand side needs to be different. By default, Cartesian coordinates are only used for curvilinear grids.

Let \(u_1,u_2,u_3\) be the primitive coordinates and \(F=BB^T\) (i.e. the inverse metric tensor), with \(B\) the change-of-coordinates matrix (see Natan et al. (2008), PRB 78, 075109, eqs. 10 and 11, i.e. the inverse Jacobian). The polynomials are given as \(u_1^{\alpha_1}u_2^{\alpha_2}u_3^{\alpha_3}\), and the right-hand side for the gradient is

1 if \(\alpha_i = 1, \alpha_j = 0, j\ne i\)
0 otherwise and for the Laplacian
\(2 F_{i,i}\) if \(\alpha_i = 2, \alpha_j = 0, j\ne i\)
\(F_{i,j} + F_{j,i}\) if \(\alpha_i = 1, \alpha_j = 1, \alpha_k = 0, k\ne i, k \ne j\)
\(H_i\) if \(\alpha_i = 1, \alpha_j = 0, j\ne i\)
0 otherwise where \(H_i=\partial^2\xi_i/(\partial x^m\partial x^m)\) is the trace of the Hessian of the coordinate transformation.

For Cartesian coordinates, the right-hand side for the Laplacian is

\(2\) if \(\alpha_i = 2, \alpha_j = 0, j\ne i\)
0 otherwise (i.e., the same as above with \(F\) as a unit matrix and \(H=0\)).

The polynomials need to include the cases for which the right-hand-side is non-zero.

The method has been tested for the default and cube stencils on all 14 Bravais lattices in 3D and yields acceptable errors for the derivatives.

Parameters

[in]	space	space (spatial and periodic dimensions)
[in]	mesh	the underlying mesh
[in]	qvector	momentum transfer for spiral BC (pass through to boundaries_oct_m::boundaries_init())

Definition at line 623 of file derivatives.F90.

◆ stencil_pol_grad()

subroutine derivatives_oct_m::stencil_pol_grad	(	integer, intent(in)	stencil_type,
		integer, intent(in)	dim,
		integer, intent(in)	direction,
		integer, intent(in)	order,
		integer, dimension(:, :), intent(inout)	polynomials
	)

private

Definition at line 693 of file derivatives.F90.

◆ stencil_pol_lapl()

subroutine derivatives_oct_m::stencil_pol_lapl	(	integer, intent(in)	stencil_type,
		type(stencil_t), intent(in)	stencil,
		integer, intent(in)	dim,
		integer, intent(in)	order,
		integer, dimension(:, :), intent(inout)	polynomials
	)

private

Definition at line 712 of file derivatives.F90.

◆ get_rhs_lapl()

subroutine derivatives_oct_m::get_rhs_lapl	(	class(coordinate_system_t), intent(in)	coord_system,
		integer, dimension(:,:), intent(in)	polynomials,
		real(real64), dimension(:), intent(in)	chi,
		real(real64), dimension(:), intent(out)	rhs,
		logical, intent(in)	stencil_primitive_coordinates
	)

private

Definition at line 732 of file derivatives.F90.

◆ get_rhs_grad()

subroutine derivatives_oct_m::get_rhs_grad	(	integer, dimension(:,:), intent(in)	polynomials,
		integer, intent(in)	dir,
		real(real64), dimension(:), intent(out)	rhs
	)

private

Definition at line 810 of file derivatives.F90.

◆ derivatives_make_discretization()

subroutine derivatives_oct_m::derivatives_make_discretization	(	type(namespace_t), intent(in)	namespace,
		type(derivatives_t), intent(in)	der,
		integer, intent(in)	nderiv,
		integer, intent(in)	ideriv,
		type(nl_operator_t), dimension(:), intent(inout)	op,
		character(len=80), intent(in), optional	name,
		logical, intent(in), optional	verbose,
		integer, intent(in), optional	order
	)

private

Definition at line 838 of file derivatives.F90.

◆ derivatives_overlap()

logical function derivatives_oct_m::derivatives_overlap ( type(derivatives_t), intent(in) this )

private

Definition at line 987 of file derivatives.F90.

◆ derivatives_get_lapl()

subroutine, public derivatives_oct_m::derivatives_get_lapl	(	type(derivatives_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		type(nl_operator_t), dimension(:), intent(inout)	op,
		class(space_t), intent(in)	space,
		character(len=80), intent(in)	name,
		integer, intent(in)	order
	)

Definition at line 999 of file derivatives.F90.

◆ derivatives_get_inner_boundary_mask()

logical function, dimension(1:this%mesh%np), public derivatives_oct_m::derivatives_get_inner_boundary_mask ( type(derivatives_t), intent(in) this )

This function tells whether a point in the grid is contained in a layer of the width of the stencil between the last row of points in the grid.

E.g. if stencil = 2, then: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 So the innermost points of the grid will not be masked, while the one between the innermost and the boundary will be masked

Returns: mask that tells which points are

Definition at line 1029 of file derivatives.F90.

◆ derivatives_lapl_get_max_eigenvalue()

real(real64) function, public derivatives_oct_m::derivatives_lapl_get_max_eigenvalue ( type(derivatives_t), intent(in) this )

Get maximum eigenvalue of discrete Laplacian. For the star and star_general stencils, use the Fourier transform of the stencil evaluated at the maximum phase to get an upper bound on the spectrum. For all other stencils, use the upper bound from the continuum.

Definition at line 1057 of file derivatives.F90.

◆ dderivatives_perform()

subroutine, public derivatives_oct_m::dderivatives_perform	(	type(nl_operator_t), intent(in), target	op,
		type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(inout), contiguous	ff,
		real(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply a nl_operator to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	op	operator to apply
[in]	der	the derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	factor	optional scaling factor

Definition at line 1166 of file derivatives.F90.

◆ dderivatives_lapl()

subroutine, public derivatives_oct_m::dderivatives_lapl	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(inout), contiguous	ff,
		real(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply the Laplacian to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	factor	optional scaling factor

Definition at line 1204 of file derivatives.F90.

◆ dderivatives_grad()

subroutine, public derivatives_oct_m::dderivatives_grad	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(inout), contiguous	ff,
		real(real64), dimension(:, :), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

apply the gradient to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function ff(1:dermeshnp_part)
[out]	op_ff	final mesh function op_ff(1:dermeshnp, 1:derdim)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	to_cartesian	flag whether conversion to cartesian coords in needed

Definition at line 1226 of file derivatives.F90.

◆ dderivatives_partial()

subroutine, public derivatives_oct_m::dderivatives_partial	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:), intent(inout), contiguous	ff,
		real(real64), dimension(:), intent(out), contiguous	op_ff,
		integer, intent(in)	dir,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the partial derivative along dir to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	dir	direction along which to calculate the partial derivative
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to set the boundary conditions (default .true.)

Definition at line 1269 of file derivatives.F90.

◆ dderivatives_div()

subroutine, public derivatives_oct_m::dderivatives_div	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:,:), intent(inout), target, contiguous	ff,
		real(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

apply the divergence operator to a vector of mesh functions

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function vector ff(1:dermeshnp_part, 1:derdim)
[out]	op_ff	final mesh function op_ff(1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	to_cartesian	flag whether conversion to cartesian coords in needed

Definition at line 1296 of file derivatives.F90.

◆ dderivatives_curl()

subroutine, public derivatives_oct_m::dderivatives_curl	(	type(derivatives_t), intent(in)	der,
		real(real64), dimension(:,:), intent(inout), contiguous	ff,
		real(real64), dimension(:,:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the curl operator to a vector of mesh functions

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function vector ff(1:dermeshnp_part, 1:derdim)
[out]	op_ff	final mesh function vector op_ff(1:dermeshnp, 1:derdim)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)

Definition at line 1362 of file derivatives.F90.

◆ dderivatives_test()

subroutine, public derivatives_oct_m::dderivatives_test	(	type(derivatives_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		integer, intent(in)	repetitions,
		integer, intent(in)	min_blocksize,
		integer, intent(in)	max_blocksize
	)

unit test for derivatives

This will be called from the test run mode.

Definition at line 1446 of file derivatives.F90.

◆ dderivatives_batch_start()

subroutine, public derivatives_oct_m::dderivatives_batch_start	(	type(nl_operator_t), intent(in), target	op,
		type(derivatives_t), intent(in), target	der,
		class(batch_t), intent(inout), target	ff,
		class(batch_t), intent(inout), target	opff,
		type(derivatives_handle_batch_t), intent(out)	handle,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply a non-local operator to a batch (1st part)

This 1st part stores important data in the handle, sets the boundaries (if requested) and starts the communication for the ghost update (if requested)

Parameters

[in]	op	the operator to be applied
[in]	der	the derivatives object
[in,out]	ff	initial batch
[in,out]	opff	finial batch (after application of the operator)
[out]	handle	handle for start/finish calls
[in]	ghost_update	whether to perform ghost updates (default=.true.)
[in]	set_bc	whether to set the boundary conditions (default=.true.)
[in]	factor	optional scaling factor

Definition at line 1713 of file derivatives.F90.

◆ dderivatives_batch_finish()

subroutine, public derivatives_oct_m::dderivatives_batch_finish	(	type(derivatives_handle_batch_t), intent(inout)	handle,
		logical, intent(in), optional	async
	)

apply a non-local operator to a batch (2nd part)

This 2nd part finished the communication and applies the operator. Here, the operator is applied to the inner points before the communication is finished, to overlap calculation and communication, if possible. After the communication is complete, the operator is applied to the outer points.

Definition at line 1766 of file derivatives.F90.

◆ dderivatives_batch_perform()

subroutine, public derivatives_oct_m::dderivatives_batch_perform	(	type(nl_operator_t), intent(in)	op,
		type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ff,
		class(batch_t), intent(inout)	opff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor,
		logical, intent(in), optional	async
	)

apply an operator to a bach of mesh functions

This is a wrapper of the corresponding start and finish routines.

Parameters

[in]	op	the operator to be applied
[in]	der	the derivatives object
[in,out]	ff	initial batch
[in,out]	opff	finial batch (after application of the operator)
[in]	ghost_update	whether to perform ghost updates (default=.true.)
[in]	set_bc	whether to set the boundary conditions (default=.true.)
[in]	factor	optional scaling factor

Definition at line 1817 of file derivatives.F90.

◆ dderivatives_batch_grad()

subroutine, public derivatives_oct_m::dderivatives_batch_grad	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		class(batch_t), dimension(:), intent(inout)	opffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian,
		real(real64), intent(in), optional	factor
	)

apply the gradient to a batch of mesh functions

Parameters

[in]	der	derivatives object
[in,out]	ffb	initial batch
[in,out]	opffb	final vector of batches
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)
[in]	to_cartesian	optional flag whether to convert to cartesian coods (currently unused)
[in]	factor	optional scaling factor

Definition at line 1844 of file derivatives.F90.

◆ dbatch_covector_to_cartesian()

subroutine derivatives_oct_m::dbatch_covector_to_cartesian	(	type(derivatives_t), intent(in)	der,
		class(coordinate_system_t), intent(in), target	coord_system,
		class(batch_t), dimension(:), intent(inout), target	uvw,
		class(batch_t), dimension(:), intent(inout), optional, target	xyz
	)

private

transform a vector of batches from affine to cartesian coordinates

Definition at line 1885 of file derivatives.F90.

◆ dderivatives_batch_curl()

subroutine, public derivatives_oct_m::dderivatives_batch_curl	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the curl to a batch of mesh functions

This routine computes first a gradient. If the gradient is known, consider using derivatives_batch_curl_from_gradient instead.

Parameters

[in]	der	the derivatives object
[in,out]	ffb	the initial batch; ffb will be overwritten by its curl
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)

Definition at line 2053 of file derivatives.F90.

◆ dderivatives_batch_curl_from_gradient()

subroutine, public derivatives_oct_m::dderivatives_batch_curl_from_gradient	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		class(batch_t), dimension(:), intent(in)	gradb
	)

calculate the curl from a batch and its gradient

If the gradient of the batch already has been calculated, this routine is reuses it to get the curl

Parameters

[in]	der	the derivatives object
[in,out]	ffb	on output: batch of the curl
[in]	gradb	batch of the gradients of the mesh functions

Definition at line 2083 of file derivatives.F90.

◆ dderivatives_batch_div()

subroutine, public derivatives_oct_m::dderivatives_batch_div	(	type(derivatives_t), intent(in)	der,
		class(batch_t), dimension(:), intent(inout)	ffb,
		class(batch_t), intent(inout)	opffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

calculate the divergence of a vector of batches

Parameters

[in]	der	the derivatives object
[in,out]	ffb	vector of initial batches
[in,out]	opffb	batch containing the divergence
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)
[in]	to_cartesian	optional flag whether to convert to cartesian coords (default .true.)

Definition at line 2148 of file derivatives.F90.

◆ zderivatives_perform()

subroutine, public derivatives_oct_m::zderivatives_perform	(	type(nl_operator_t), intent(in), target	op,
		type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:), intent(inout), contiguous	ff,
		complex(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply a nl_operator to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	op	operator to apply
[in]	der	the derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	factor	optional scaling factor

Definition at line 2281 of file derivatives.F90.

◆ zderivatives_lapl()

subroutine, public derivatives_oct_m::zderivatives_lapl	(	type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:), intent(inout), contiguous	ff,
		complex(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply the Laplacian to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	factor	optional scaling factor

Definition at line 2319 of file derivatives.F90.

◆ zderivatives_grad()

subroutine, public derivatives_oct_m::zderivatives_grad	(	type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:), intent(inout), contiguous	ff,
		complex(real64), dimension(:, :), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

apply the gradient to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function ff(1:dermeshnp_part)
[out]	op_ff	final mesh function op_ff(1:dermeshnp, 1:derdim)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	to_cartesian	flag whether conversion to cartesian coords in needed

Definition at line 2341 of file derivatives.F90.

◆ zderivatives_partial()

subroutine, public derivatives_oct_m::zderivatives_partial	(	type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:), intent(inout), contiguous	ff,
		complex(real64), dimension(:), intent(out), contiguous	op_ff,
		integer, intent(in)	dir,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the partial derivative along dir to a mesh function

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function (1:dermeshnp_part)
[out]	op_ff	final mesh function (1:dermeshnp)
[in]	dir	direction along which to calculate the partial derivative
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to set the boundary conditions (default .true.)

Definition at line 2384 of file derivatives.F90.

◆ zderivatives_div()

subroutine, public derivatives_oct_m::zderivatives_div	(	type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:,:), intent(inout), target, contiguous	ff,
		complex(real64), dimension(:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

apply the divergence operator to a vector of mesh functions

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function vector ff(1:dermeshnp_part, 1:derdim)
[out]	op_ff	final mesh function op_ff(1:dermeshnp)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)
[in]	to_cartesian	flag whether conversion to cartesian coords in needed

Definition at line 2411 of file derivatives.F90.

◆ zderivatives_curl()

subroutine, public derivatives_oct_m::zderivatives_curl	(	type(derivatives_t), intent(in)	der,
		complex(real64), dimension(:,:), intent(inout), contiguous	ff,
		complex(real64), dimension(:,:), intent(out), contiguous	op_ff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the curl operator to a vector of mesh functions

Note: the initial mesh function needs to be defined including ghost and boundary points! As the ghost points are updated, the initial mesh function needs to be declared intent(inout).

Parameters

[in]	der	derivatives object
[in,out]	ff	initial mesh function vector ff(1:dermeshnp_part, 1:derdim)
[out]	op_ff	final mesh function vector op_ff(1:dermeshnp, 1:derdim)
[in]	ghost_update	flag whether to perform the ghost update (default .true.)
[in]	set_bc	flag whether to apply the boundary conditions (default .true.)

Definition at line 2477 of file derivatives.F90.

◆ zderivatives_test()

subroutine, public derivatives_oct_m::zderivatives_test	(	type(derivatives_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		integer, intent(in)	repetitions,
		integer, intent(in)	min_blocksize,
		integer, intent(in)	max_blocksize
	)

unit test for derivatives

This will be called from the test run mode.

Definition at line 2561 of file derivatives.F90.

◆ zderivatives_batch_start()

subroutine, public derivatives_oct_m::zderivatives_batch_start	(	type(nl_operator_t), intent(in), target	op,
		type(derivatives_t), intent(in), target	der,
		class(batch_t), intent(inout), target	ff,
		class(batch_t), intent(inout), target	opff,
		type(derivatives_handle_batch_t), intent(out)	handle,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor
	)

apply a non-local operator to a batch (1st part)

This 1st part stores important data in the handle, sets the boundaries (if requested) and starts the communication for the ghost update (if requested)

Parameters

[in]	op	the operator to be applied
[in]	der	the derivatives object
[in,out]	ff	initial batch
[in,out]	opff	finial batch (after application of the operator)
[out]	handle	handle for start/finish calls
[in]	ghost_update	whether to perform ghost updates (default=.true.)
[in]	set_bc	whether to set the boundary conditions (default=.true.)
[in]	factor	optional scaling factor

Definition at line 2836 of file derivatives.F90.

◆ zderivatives_batch_finish()

subroutine, public derivatives_oct_m::zderivatives_batch_finish	(	type(derivatives_handle_batch_t), intent(inout)	handle,
		logical, intent(in), optional	async
	)

apply a non-local operator to a batch (2nd part)

This 2nd part finished the communication and applies the operator. Here, the operator is applied to the inner points before the communication is finished, to overlap calculation and communication, if possible. After the communication is complete, the operator is applied to the outer points.

Definition at line 2889 of file derivatives.F90.

◆ zderivatives_batch_perform()

subroutine, public derivatives_oct_m::zderivatives_batch_perform	(	type(nl_operator_t), intent(in)	op,
		type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ff,
		class(batch_t), intent(inout)	opff,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		real(real64), intent(in), optional	factor,
		logical, intent(in), optional	async
	)

apply an operator to a bach of mesh functions

This is a wrapper of the corresponding start and finish routines.

Parameters

[in]	op	the operator to be applied
[in]	der	the derivatives object
[in,out]	ff	initial batch
[in,out]	opff	finial batch (after application of the operator)
[in]	ghost_update	whether to perform ghost updates (default=.true.)
[in]	set_bc	whether to set the boundary conditions (default=.true.)
[in]	factor	optional scaling factor

Definition at line 2940 of file derivatives.F90.

◆ zderivatives_batch_grad()

subroutine, public derivatives_oct_m::zderivatives_batch_grad	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		class(batch_t), dimension(:), intent(inout)	opffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian,
		real(real64), intent(in), optional	factor
	)

apply the gradient to a batch of mesh functions

Parameters

[in]	der	derivatives object
[in,out]	ffb	initial batch
[in,out]	opffb	final vector of batches
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)
[in]	to_cartesian	optional flag whether to convert to cartesian coods (currently unused)
[in]	factor	optional scaling factor

Definition at line 2967 of file derivatives.F90.

◆ zbatch_covector_to_cartesian()

subroutine derivatives_oct_m::zbatch_covector_to_cartesian	(	type(derivatives_t), intent(in)	der,
		class(coordinate_system_t), intent(in), target	coord_system,
		class(batch_t), dimension(:), intent(inout), target	uvw,
		class(batch_t), dimension(:), intent(inout), optional, target	xyz
	)

private

transform a vector of batches from affine to cartesian coordinates

Definition at line 3008 of file derivatives.F90.

◆ zderivatives_batch_curl()

subroutine, public derivatives_oct_m::zderivatives_batch_curl	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc
	)

apply the curl to a batch of mesh functions

This routine computes first a gradient. If the gradient is known, consider using derivatives_batch_curl_from_gradient instead.

Parameters

[in]	der	the derivatives object
[in,out]	ffb	the initial batch; ffb will be overwritten by its curl
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)

Definition at line 3176 of file derivatives.F90.

◆ zderivatives_batch_curl_from_gradient()

subroutine, public derivatives_oct_m::zderivatives_batch_curl_from_gradient	(	type(derivatives_t), intent(in)	der,
		class(batch_t), intent(inout)	ffb,
		class(batch_t), dimension(:), intent(in)	gradb
	)

calculate the curl from a batch and its gradient

If the gradient of the batch already has been calculated, this routine is reuses it to get the curl

Parameters

[in]	der	the derivatives object
[in,out]	ffb	on output: batch of the curl
[in]	gradb	batch of the gradients of the mesh functions

Definition at line 3206 of file derivatives.F90.

◆ zderivatives_batch_div()

subroutine, public derivatives_oct_m::zderivatives_batch_div	(	type(derivatives_t), intent(in)	der,
		class(batch_t), dimension(:), intent(inout)	ffb,
		class(batch_t), intent(inout)	opffb,
		logical, intent(in), optional	ghost_update,
		logical, intent(in), optional	set_bc,
		logical, intent(in), optional	to_cartesian
	)

calculate the divergence of a vector of batches

Parameters

[in]	der	the derivatives object
[in,out]	ffb	vector of initial batches
[in,out]	opffb	batch containing the divergence
[in]	ghost_update	optional flag whether to perform the ghost update (default .true.)
[in]	set_bc	optional flag whether to set the boundary conditions (default .true.)
[in]	to_cartesian	optional flag whether to convert to cartesian coords (default .true.)

Definition at line 3271 of file derivatives.F90.

Variable Documentation

◆ der_bc_zero_f

integer, parameter derivatives_oct_m::der_bc_zero_f = 0

private

function is zero at the boundaries

Definition at line 210 of file derivatives.F90.

◆ der_bc_zero_df

integer, parameter derivatives_oct_m::der_bc_zero_df = 1

private

first derivative of the function is zero

Definition at line 210 of file derivatives.F90.

◆ der_bc_period

integer, parameter derivatives_oct_m::der_bc_period = 2

private

boundary is periodic

Definition at line 210 of file derivatives.F90.

◆ der_star

integer, parameter, public derivatives_oct_m::der_star = 1

Definition at line 215 of file derivatives.F90.

◆ der_variational

integer, parameter, public derivatives_oct_m::der_variational = 2

Definition at line 215 of file derivatives.F90.

◆ der_cube

integer, parameter, public derivatives_oct_m::der_cube = 3

Definition at line 215 of file derivatives.F90.

◆ der_starplus

integer, parameter, public derivatives_oct_m::der_starplus = 4

Definition at line 215 of file derivatives.F90.

◆ der_stargeneral

integer, parameter, public derivatives_oct_m::der_stargeneral = 5

Definition at line 215 of file derivatives.F90.

◆ blocking

integer, parameter derivatives_oct_m::blocking = 1

private

Definition at line 222 of file derivatives.F90.

◆ non_blocking

integer, parameter derivatives_oct_m::non_blocking = 2

private

Definition at line 222 of file derivatives.F90.

◆ kernel_uvw_xyz

type(accel_kernel_t) derivatives_oct_m::kernel_uvw_xyz

private

Definition at line 276 of file derivatives.F90.

◆ kernel_dcurl

type(accel_kernel_t) derivatives_oct_m::kernel_dcurl

private

Definition at line 276 of file derivatives.F90.

◆ kernel_zcurl

type(accel_kernel_t) derivatives_oct_m::kernel_zcurl

private

Definition at line 276 of file derivatives.F90.

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ derivatives_init()

◆ derivatives_end()

◆ derivatives_get_stencil_lapl()

◆ derivatives_lapl_diag()

◆ derivatives_get_stencil_grad()

◆ derivatives_build()

◆ stencil_pol_grad()

◆ stencil_pol_lapl()

◆ get_rhs_lapl()

◆ get_rhs_grad()

◆ derivatives_make_discretization()

◆ derivatives_overlap()

◆ derivatives_get_lapl()

◆ derivatives_get_inner_boundary_mask()

◆ derivatives_lapl_get_max_eigenvalue()

◆ dderivatives_perform()

◆ dderivatives_lapl()

◆ dderivatives_grad()

◆ dderivatives_partial()

◆ dderivatives_div()

◆ dderivatives_curl()

◆ dderivatives_test()

◆ dderivatives_batch_start()

◆ dderivatives_batch_finish()

◆ dderivatives_batch_perform()

◆ dderivatives_batch_grad()

◆ dbatch_covector_to_cartesian()

◆ dderivatives_batch_curl()

◆ dderivatives_batch_curl_from_gradient()

◆ dderivatives_batch_div()

◆ zderivatives_perform()

◆ zderivatives_lapl()

◆ zderivatives_grad()

◆ zderivatives_partial()

◆ zderivatives_div()

◆ zderivatives_curl()

◆ zderivatives_test()

◆ zderivatives_batch_start()

◆ zderivatives_batch_finish()

◆ zderivatives_batch_perform()

◆ zderivatives_batch_grad()

◆ zbatch_covector_to_cartesian()

◆ zderivatives_batch_curl()

◆ zderivatives_batch_curl_from_gradient()

◆ zderivatives_batch_div()

Variable Documentation

◆ der_bc_zero_f

◆ der_bc_zero_df

◆ der_bc_period

◆ der_star

◆ der_variational

◆ der_cube

◆ der_starplus

◆ der_stargeneral

◆ blocking

◆ non_blocking

◆ kernel_uvw_xyz

◆ kernel_dcurl

◆ kernel_zcurl