vac_utilities Module Reference

Numerical utilities related to the vacuum response. More...

Functions/Subroutines
subroutine, public	calc_gh_int_1 (G, H, x_s, x_in, norm_s, h_fac_in, step_size, tol)
	Calculate G_ij and H_ij on an interval for field line aligned configurations. More...
subroutine, public	calc_gh_int_2 (G, H, t_s, t_in, x_s, x_in, norm_s, norm_in, Aij, ql, tol, b_coeff, n_tor)
	Calculate G_ij and H_ij on an interval for axisymmetric configurations. More...
integer function, public	vec_dis2loc (ctxt, vec_dis, lims, vec_loc, proc)
	Gathers a distributed vector on a single process. More...
integer function, public	mat_dis2loc (ctxt, mat_dis, lims_r, lims_c, mat_loc, proc)
	Gathers a distributed vector on a single process. More...
integer function, public	interlaced_vac_copy (vac_old, vac)
	Copies vacuum variables of a previous level into the appropriate, interlaced place of a next level. More...

Detailed Description

Numerical utilities related to the vacuum response.

See also

vac_ops for information.

Function/Subroutine Documentation

calc_gh_int_1()

subroutine, public vac_utilities::calc_gh_int_1	(	real(dp), dimension(2), intent(inout)	G,
		real(dp), dimension(2), intent(inout)	H,
		real(dp), dimension(2,3), intent(in)	x_s,
		real(dp), dimension(3), intent(in)	x_in,
		real(dp), dimension(2,3), intent(in)	norm_s,
		real(dp), dimension(4), intent(in)	h_fac_in,
		real(dp), dimension(2), intent(in)	step_size,
		real(dp), intent(in)	tol
	)

Calculate G_ij and H_ij on an interval for field line aligned configurations.

The indices for the source variables are [left:right,dim] where dim is the Cartesian dimension. The same holds for ql.

For subintegrals close to the singularity, the procedure uses the analytical approximation.

Note

This routine does not calculate the contribution \(2\beta\).

Parameters

[in]	x_s	position vector at left and right limit of source interval
[in]	x_in	position vector at which to calculate influence
[in]	norm_s	normal vector at left and right limit of source interval
[in]	h_fac_in	metric factors at which to calculate influence
[in]	step_size	step sizes in parallel direction and alpha
[in]	tol	tolerance on distance between points

Definition at line 33 of file vac_utilities.f90.

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calc_gh_int_2()

subroutine, public vac_utilities::calc_gh_int_2	(	real(dp), dimension(2), intent(inout)	G,
		real(dp), dimension(2), intent(inout)	H,
		real(dp), dimension(2), intent(in)	t_s,
		real(dp), intent(in)	t_in,
		real(dp), dimension(2,2), intent(in)	x_s,
		real(dp), dimension(2), intent(in)	x_in,
		real(dp), dimension(2,2), intent(in)	norm_s,
		real(dp), dimension(2), intent(in)	norm_in,
		real(dp), dimension(2), intent(in)	Aij,
		real(dp), dimension(2,2), intent(in)	ql,
		real(dp), intent(in)	tol,
		real(dp), dimension(2), intent(in)	b_coeff,
		integer, intent(in)	n_tor
	)

Calculate G_ij and H_ij on an interval for axisymmetric configurations.

The indices for the source variables are [left:right,dim] where dim is the Cartesian dimension. The same holds for ql.

For subintegrals close to the singularity (i.e. where the tolerance is no being met), the routine approximates the toroidal functions with the analytical approximation. If one of the boundaries of the subintegral is far enough from the singularity, there is an additional contribution due to the difference between the actual toroidal function and the approximation. This contribution is zero if both boundaries are close, because in this case it is assumed that the entire integral is given by the analytical approximation.

Note

This routine does not calculate the contribution \(2\beta\).

Parameters

[in]	t_s	pol. angle at left and right limit of source interval
[in]	t_in	pol. angle at which to calculate influence
[in]	x_s	position vector at left and right limit of source interval
[in]	x_in	position vector at which to calculate influence
[in]	norm_s	normal vector at left and right limit of source interval
[in]	norm_in	normal vector at which to calculate influence
[in]	aij	Aij helper variable for H
[in]	ql	ql for n-1 and n at left and right limit of source interval
[in]	tol	tolerance on rho2
[in]	b_coeff	\(b = \sum_{k=1}^n \frac{2}{2k-1}\) for n and n-1
[in]	n_tor	toroidal mode number

Definition at line 99 of file vac_utilities.f90.

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interlaced_vac_copy()

integer function, public vac_utilities::interlaced_vac_copy	(	type(vac_type), intent(in)	vac_old,
		type(vac_type), intent(inout)	vac
	)

Copies vacuum variables of a previous level into the appropriate, interlaced place of a next level.

This is done by multiplying left by \(\overline{\text{T}}\) and right by \(\overline{\text{T}}^T\) with

\[ a_{ij} = \left\{\begin{aligned} 1 \quad &\text{for} \left(i,j\right) = \left(2j-1+(i-1)n_\text{old},j+(i-1)n_\text{old}\right) \\ 0 \quad &\text{otherwise} \end{aligned}\right. \]

where \(i\) ranges from \(1\) to \(n_\text{old}\) and \(j\) from \(1\) to \(m_\text{old}\), with the size of \(\overline{\text{T}}\) equal to \(n_\text{new} \times n_\text{old} \) where \(n\) refers to n_bnd(1) and \(m\) to n_bnd(2).

Parameters

[in]	vac_old	old vacuum
[in,out]	vac	vacuum

Definition at line 355 of file vac_utilities.f90.

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mat_dis2loc()

integer function, public vac_utilities::mat_dis2loc	(	integer, intent(in)	ctxt,
		real(dp), dimension(:,:), intent(in)	mat_dis,
		integer, dimension(:,:), intent(in)	lims_r,
		integer, dimension(:,:), intent(in)	lims_c,
		real(dp), dimension(:,:), intent(inout)	mat_loc,
		integer, intent(in), optional	proc
	)

Gathers a distributed vector on a single process.

See also

See vec_dis2loc() for exaplanation.

Parameters

[in]	ctxt	context for matrix
[in]	mat_dis	distributed matrix
[in]	lims_r	limits for different subrows
[in]	lims_c	limits for different subcolumns
[in,out]	mat_loc	local matrix
[in]	proc	which process receives result

Definition at line 277 of file vac_utilities.f90.

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vec_dis2loc()

integer function, public vac_utilities::vec_dis2loc	(	integer, intent(in)	ctxt,
		real(dp), dimension(:), intent(in)	vec_dis,
		integer, dimension(:,:), intent(in)	lims,
		real(dp), dimension(:), intent(inout)	vec_loc,
		integer, intent(in), optional	proc
	)

Gathers a distributed vector on a single process.

For the distributed vector, the limits of the different subrows need to be provided, as discussed in init_vac().

By default, the result lands on the master process, but this can be changed using proc. If it is negative, all processes receive the result. In any case, vec_loc will be utilized.

Note

vec_loc needs to be allocated to the total dimensions, even when the results is not received by the process.

Parameters

[in]	ctxt	context for vector
[in]	vec_dis	distributed vector
[in]	lims	limits for different subrows
[in,out]	vec_loc	local vector
[in]	proc	which process receives result

Definition at line 223 of file vac_utilities.f90.

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