utilities Module Reference

This file contains utilities for converting the siesta grids. More...

Data Types
interface	to_full_mesh
	Interface to convert between half and full mesh using either to_full_mesh2 or to_full_mesh3. More...
interface	to_half_mesh
	Interface to convert between full and half mesh using either to_half_mesh or to_half_mesh_p. More...
interface	gradienthalf
	Interface to take the gradianet from full to half mesh using either GradientHalf or GradientHalf_p. More...
interface	curl_htof
	Interface to take the curl on a half mesh quantity and return a full mesh using either curl_htof or curl_htof_targ. More...
interface	set_bndy_fouier_m0
	Interface to set the fouier conditions on a quantity for either scalar set_bndy_fouier_m0 or vector set_bndy_fouier_m0_vec quantities. More...

Functions/Subroutines
subroutine	gradienthalf (gradienth, vecf)
	Calculate the gradient to the half mesh from a full mesh quantity. More...
subroutine	gradienthalf_p (gradienth, vecf)
	Calculate the gradient to the half mesh from a full mesh quantity. More...
subroutine	gradientfull (gradientf, vech)
	Calculate the gradient to the full mesh from a half mesh quantity. More...
subroutine	to_half_mesh (vecf, vech)
	Migrates a full mesh quantity to the half mesh. More...
subroutine	to_half_mesh_p (vecf, vech)
	Migrates a full mesh quantity to the half mesh. More...
subroutine	to_full_mesh3 (vech, vecf)
	Migrate a three dimensional quantity form the half mesh to the full mesh. More...
subroutine	to_full_mesh2 (vech, vecf)
	Migrate a two dimensional quantity form the half mesh to the full mesh. More...
subroutine	curl_ftoh (asubsmnf, asubumnf, asubvmnf,
	Compute curl of the full grid quantity a on the half grid. More...
subroutine	curl_htof (bsubsmnh, bsubumnh, bsubvmnh,
	Compute curl of the half grid quantity a on the full grid. More...
subroutine	curl_htof_targ (bsubsmnh, bsubumnh, bsubvmnh,
	Convert allocatable to pointer for use in curl_htof. More...
pure subroutine	set_bndy_half_to_full (amnh, amnf, nsmin, parity, f
	Set fouier boundary conditions for full grid quantity converted from half grid. More...
pure subroutine	set_bndy_half_to_full_ds (amnh, amnf_ds, nsmin, par
	Set fouier boundary conditions for full grid radial derivative quantity converted from half grid. More...
pure subroutine	set_bndy_full_origin (amnsf, amnuf, amnvf, flags)
	Apply origin vector boundary conditions. More...
pure subroutine	set_bndy_fouier_m0 (amn, parity)
	Set vector fourier conditions. More...
pure subroutine	set_bndy_fouier_m0_vec (amns, amnu, amnv, parity)
	Set vector fourier conditions. More...
subroutine	div_h (jbsupsmnh, jbsupumnh, jbsupvmnh,
	Compute the divergence of a half grid quantity. More...
logical function	test_utilities ()
	Test utility routines. More...
logical function	test_div (jbsupsmnh, jbsupumnh, jbsupvmnh, parity, nsmin,
	Test divergence of a half grid quantity. More...

Detailed Description

This file contains utilities for converting the siesta grids.

Function/Subroutine Documentation

curl_ftoh()

subroutine utilities::curl_ftoh	(		asubsmnf,
			asubumnf,
			asubvmnf
	)

Compute curl of the full grid quantity a on the half grid.

The contravariant components of jac*Curl A are equal to

sqrt(g)*B^k = dA_j/du^i - dA_i/du^j (j)

for cyclic permutations of i,j,k. This routine does not remove the jacobian factor. The arrays must be passed in as ALLOCATABLE or POINTER to preserve the array bounds.

Parameters

[in]	asubsmnf	Covariant vector in the s direction full grid.
[in]	asubsmnf	Covariant vector in the u direction full grid.
[in]	asubsmnf	Covariant vector in the v direction full grid.
[in,out]	jbsubsmnh	Contravariant vector in the s direction with jacobian factor half grid.
[in,out]	jbsubsmnh	Contravariant vector in the u direction with jacobian factor half grid.
[in,out]	jbsubsmnh	Contravariant vector in the v direction with jacobian factor half grid.
[in]	parity	Parity flag.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.

curl_htof()

subroutine utilities::curl_htof	(	real (dp), dimension(:,:,:), intent(in), allocatable	bsubsmnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	bsubumnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	bsubvmnh
	)

Compute curl of the half grid quantity a on the full grid.

The contravariant components of jac*Curl A are equal to

sqrt(g)*K^k = dB_j/du^i - dB_i/du^j (j)

for cyclic permutations of i,j,k. This routine does not remove the jacobian factor. The arrays must be passed in as ALLOCATABLE or POINTER to preserve the array bounds.

Parameters

[in]	bsubsmnh	Covariant vector in the s direction half grid.
[in]	bsubsmnh	Covariant vector in the u direction half grid.
[in]	bsubsmnh	Covariant vector in the v direction half grid.
[in,out]	jKsubsmnf	Contravariant vector in the s direction with jacobian factor full grid.
[in,out]	jKsubsmnf	Contravariant vector in the u direction with jacobian factor full grid.
[in,out]	jKsubsmnf	Contravariant vector in the v direction with jacobian factor full grid.
[in]	parity	Parity flag.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.
[in]	nsend	Ending row index.
[in,out]	curtor	Current enclosed at the boundary.

curl_htof_targ()

subroutine utilities::curl_htof_targ	(	real (dp), dimension(:,:,:), intent(in), allocatable	bsubsmnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	bsubumnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	bsubvmnh
	)

Convert allocatable to pointer for use in curl_htof.

Parameters

[in]	Asubsmnh	Covariant vector in the s direction half grid.
[in]	Asubsmnh	Covariant vector in the u direction half grid.
[in]	Asubsmnh	Covariant vector in the v direction half grid.
[in,out]	jBsubsmnf	Contravariant vector in the s direction with jacobian factor full grid.
[in,out]	jBsubsmnf	Contravariant vector in the u direction with jacobian factor full grid.
[in,out]	jBsubsmnf	Contravariant vector in the v direction with jacobian factor full grid.
[in]	parity	Parity flag.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.
[in]	nsend	Ending row index.
[in,out]	curtor	Current enclosed at the boundary.

div_h()

subroutine utilities::div_h	(		jbsupsmnh,
			jbsupumnh,
			jbsupvmnh
	)

Compute the divergence of a half grid quantity.

This operator is used for unit testing of the curl operator. Divergence is defined as

DIV(B) = 1/sqrt(g)d/dx (JB^x} for x = s,u,v (1)

Note for testing that divergence remains zero, add a 1/sqrt(g) term is not necessary to retain.

Parameters

[in]	jasupsmnh	Contravariant vector in the s direction half grid.
[in]	jasupsmnh	Contravariant vector in the u direction half grid.
[in]	jasupsmnh	Contravariant vector in the v direction half grid.
[in,out]	divmnf	Diverence on the full grid.
[in]	parity	Parity flag.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.

gradientfull()

subroutine utilities::gradientfull	(		gradientf,
		real (dp), dimension(:,:,:), intent(in), allocatable	vech
	)

Calculate the gradient to the full mesh from a half mesh quantity.

The arrays must be passed in as ALLOCATABLE to preserve the array bounds. There are three scenarios we need to anticipate for the radial dimension. The easiest is when the upper bound of gradientf matches vech. Otherwise vech can be the full ns range of one more than the gradientf. To handle this an extra is calculated which can be a maximum of one.

Parameters

[in,out]	gradientf	Gradient on the full grid.
[in]	vech	Half grid quantity.

gradienthalf()

subroutine utilities::gradienthalf	(		gradienth,
		real (dp), dimension(:,:,:), intent(in), allocatable	vecf
	)

Calculate the gradient to the half mesh from a full mesh quantity.

The arrays must be passed in as ALLOCATABLE to preserve the array bounds.

Parameters

[in,out]	gradienth	Gradient on the half grid.
[in]	vecf	Full grid quantity.

gradienthalf_p()

subroutine utilities::gradienthalf_p	(		gradienth,
		real (dp), dimension(:,:,:), pointer	vecf
	)

Calculate the gradient to the half mesh from a full mesh quantity.

The arrays must be passed in as ALLOCATABLE to preserve the array bounds. Full vector is passed in as a pointer.

Parameters

[in,out]	gradienth	Gradient on the half grid.
[in]	vecf	Full grid quantity.

set_bndy_fouier_m0()

pure subroutine utilities::set_bndy_fouier_m0	(	real (dp), dimension(:,:,:), intent(inout)	amn,
		integer, intent(in)	parity
	)

Set vector fourier conditions.

For fouier modes for m=0 and for the negative n modes. The n=0 modes are zero for quantities with sin parity.

Parameters

[in,out]	amn	Fourier quantity.
[in]	parity	Fouier parity flag.

set_bndy_fouier_m0_vec()

pure subroutine utilities::set_bndy_fouier_m0_vec	(	real (dp), dimension(:,:,:), intent(inout)	amns,
		real (dp), dimension(:,:,:), intent(inout)	amnu,
		real (dp), dimension(:,:,:), intent(inout)	amnv,
		integer, intent(in)	parity
	)

Set vector fourier conditions.

For fouier modes for m=0 and for the negative n modes. The n=0 modes are zero for quantities with sin parity.

Parameters

[in,out]	amns	Fourier quantity for s component.
[in,out]	amnu	Fourier quantity for u component.
[in,out]	amnv	Fourier quantity for v component.
[in]	parity	Fouier parity flag.

set_bndy_full_origin()

pure subroutine utilities::set_bndy_full_origin	(	real (dp), dimension(:,:,:), intent(inout)	amnsf,
		real (dp), dimension(:,:,:), intent(inout)	amnuf,
		real (dp), dimension(:,:,:), intent(inout)	amnvf,
		integer, intent(in)	flags
	)

Apply origin vector boundary conditions.

At the center of the grid, a vector quantity should have only m=1 modes in the s direction, no modes in the u direction and only m=0 modes in the v direction. See siesta_init::GetFields.

Parameters

[in,out]	amnsf	Full grid fourier quantity for s component.
[in,out]	amnuf	Full grid fourier quantity for u component.
[in,out]	amnvf	Full grid fourier quantity for v component.
[in]	flags	Control flags.

set_bndy_half_to_full()

pure subroutine utilities::set_bndy_half_to_full	(	real (dp), dimension(:,:,:), intent(in)	amnh,
		real (dp), dimension(:,:,:), intent(inout)	amnf,
		integer, intent(in)	nsmin,
		integer, intent(in)	parity,
			f
	)

Set fouier boundary conditions for full grid quantity converted from half grid.

At the center of the grid, the quantity should not be a function of u so all m > 0 modes should be zero. For the m = 0 terms, use the value from the half grid.

Parameters

[in]	amnh	Half grid fourier quantity.
[in,out]	amnf	Full grid fourier quantity.
[in]	nsmin	Minimum radial index.
[in]	parity	Parity flag.
[in]	flags	Control flags.

set_bndy_half_to_full_ds()

pure subroutine utilities::set_bndy_half_to_full_ds	(	real (dp), dimension(:,:,:), intent(in)	amnh,
		real (dp), dimension(:,:,:), intent(inout)	amnf_ds,
		integer, intent(in)	nsmin,
			par
	)

Set fouier boundary conditions for full grid radial derivative quantity converted from half grid.

At the center of the grid the the m=1 quanity flips size across the s=0 point. The results in a doubling of the m=1 component for the first half grid.

Parameters

[in]	amnh	Half grid fourier quantity.
[in,out]	amnf_ds	Full grid radial derivative fourier quantity.
[in]	nsmin	Minimum radial index.
[in]	parity	Parity flag.
[in]	flags	Control flags.

test_div()

logical function utilities::test_div	(	real (dp), dimension(:,:,:), intent(in), allocatable	jbsupsmnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	jbsupumnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	jbsupvmnh,
		integer, intent(in)	parity,
		integer, intent(in)	nsmin
	)

Test divergence of a half grid quantity.

Parameters

[in]	jbsupsmnh	Contravariant vector in the s direction half grid.
[in]	jbsupumnh	Contravariant vector in the u direction half grid.
[in]	jbsupvmnh	Contravariant vector in the v direction half grid.
[in]	parity	Parity flag.
[in]	nsmin	Minimum radial index.
[in]	nsmax	Maximum radial index.

test_utilities()

logical function utilities::test_utilities

Test utility routines.

Test the various operations of in the utilities module. Current tests check:

• Check the div(curl(A)) is identially zero.

to_full_mesh2()

subroutine utilities::to_full_mesh2	(	real (dp), dimension(:,:), intent(in), allocatable	vech,
		real (dp), dimension(:,:), intent(inout), allocatable	vecf
	)

Migrate a two dimensional quantity form the half mesh to the full mesh.

First and last point are extrapolated linearly. The arrays must be passed in as ALLOCATABLE to preserve the array bounds.

Parameters

[in]	vech	Half mesh qantity.
[in,out]	vecf	Full mesh quantity.

to_full_mesh3()

subroutine utilities::to_full_mesh3	(	real (dp), dimension(:,:,:), intent(in), allocatable	vech,
		real (dp), dimension(:,:,:), intent(inout), allocatable	vecf
	)

Migrate a three dimensional quantity form the half mesh to the full mesh.

First and last point are extrapolated linearly. The arrays must be passed in as ALLOCATABLE to preserve the array bounds.

Parameters

[in]	vech	Half mesh qantity.
[in,out]	vecf	Full mesh quantity.

to_half_mesh()

subroutine utilities::to_half_mesh	(	real (dp), dimension(:,:,:), intent(in), allocatable	vecf,
		real (dp), dimension(:,:,:), intent(inout), allocatable	vech
	)

Migrates a full mesh quantity to the half mesh.

The arrays must be passed in as ALLOCATABLE to preserve the array bounds.

Parameters

[in]	vecf	Full grid quantity.
[in,out]	vech	Half grid quantity.

to_half_mesh_p()

subroutine utilities::to_half_mesh_p	(	real (dp), dimension(:,:,:), pointer	vecf,
		real (dp), dimension(:,:,:), intent(inout), allocatable	vech
	)

Migrates a full mesh quantity to the half mesh.

The arrays must be passed in as ALLOCATABLE to preserve the array bounds. Full vector grid is passed in as pointer.

Parameters

[in]	vecf	Full grid quantity.
[in,out]	vech	Half grid quantity.