Vector potential and the Beltrami linear system

Collaboration diagram for Vector potential and the Beltrami linear system:

Variables
integer, dimension(:), allocatable	allglobal::nadof
	degrees of freedom in Beltrami fields in each annulus
integer, dimension(:), allocatable	allglobal::nfielddof
	degrees of freedom in Beltrami fields in each annulus, field only, no Lagrange multipliers
type(subgrid), dimension(:,:,:), allocatable	allglobal::ate
	magnetic vector potential cosine Fourier harmonics; stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::aze
	magnetic vector potential cosine Fourier harmonics; stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::ato
	magnetic vector potential sine Fourier harmonics; non-stellarator-symmetric
type(subgrid), dimension(:,:,:), allocatable	allglobal::azo
	magnetic vector potential sine Fourier harmonics; non-stellarator-symmetric
integer, dimension(:,:), allocatable	allglobal::lma
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmb
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmc
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmd
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lme
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmf
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmg
	Lagrange multipliers (?)
integer, dimension(:,:), allocatable	allglobal::lmh
	Lagrange multipliers (?)
real, dimension(:,:), allocatable	allglobal::lmavalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmbvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmcvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmdvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmevalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmfvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmgvalue
	what is this?
real, dimension(:,:), allocatable	allglobal::lmhvalue
	what is this?
integer, dimension(:,:), allocatable	allglobal::fso
	what is this?
integer, dimension(:,:), allocatable	allglobal::fse
	what is this?
logical	allglobal::lcoordinatesingularity
	set by LREGION macro; true if inside the innermost volume
logical	allglobal::lplasmaregion
	set by LREGION macro; true if inside the plasma region
logical	allglobal::lvacuumregion
	set by LREGION macro; true if inside the vacuum region
logical	allglobal::lsavedguvij
	flag used in matrix free
logical	allglobal::localconstraint
	what is this?

Detailed Description

• In each volume, the total degrees of freedom in the Beltrami linear system is NAdof(1:Nvol). This depends on Mpol, Ntor and Lrad(vvol).
• The covariant components of the vector potential are written as

  \begin{eqnarray} A_\theta & = & \sum_i \sum_{l=0}^L {\color{red} A_{\theta,e,i,l}} \; T_{l}(s) \cos\alpha_i + \sum_i \sum_{l=0}^L {\color{Orange} A_{\theta,o,i,l}} \; T_{l}(s) \sin\alpha_i \\ A_\zeta & = & \sum_i \sum_{l=0}^L {\color{blue} A_{\zeta, e,i,l}} \; T_{l}(s) \cos\alpha_i + \sum_i \sum_{l=0}^L {\color{Cerulean}A_{\zeta ,o,i,l}} \; T_{l}(s) \sin\alpha_i , \end{eqnarray}

  where \(T_l(s)\) are the Chebyshev polynomials and \(\alpha_i \equiv m_i \theta - n_i \zeta\).

• The following internal arrays are declared in preset() :

  dAte(0,i)%s(l) \(\equiv {\color{red} A_{\theta,e,i,l}}\)

  dAze(0,i)%s(l) \(\equiv {\color{blue} A_{\zeta, e,i,l}}\)

  dAto(0,i)%s(l) \(\equiv {\color{Orange} A_{\theta,o,i,l}}\)

  dAzo(0,i)%s(l) \(\equiv {\color{Cerulean}A_{\zeta ,o,i,l}}\)