Field matrices: dMA, dMB, dMC, dMD, dME, dMF

Collaboration diagram for Field matrices: dMA, dMB, dMC, dMD, dME, dMF:

Variables
real, dimension(:,:), allocatable	allglobal::dma
	energy and helicity matrices; quadratic forms
real, dimension(:,:), allocatable	allglobal::dmb
	energy and helicity matrices; quadratic forms
real, dimension(:,:), allocatable	allglobal::dmd
	energy and helicity matrices; quadratic forms
real, dimension(:), allocatable	allglobal::dmas
	sparse version of dMA, data
real, dimension(:), allocatable	allglobal::dmds
	sparse version of dMD, data
integer, dimension(:), allocatable	allglobal::idmas
	sparse version of dMA and dMD, indices
integer, dimension(:), allocatable	allglobal::jdmas
	sparse version of dMA and dMD, indices
integer, dimension(:), allocatable	allglobal::ndmasmax
	number of elements for sparse matrices
integer, dimension(:), allocatable	allglobal::ndmas
	number of elements for sparse matrices
real, dimension(:), allocatable	allglobal::dmg
	what is this?
real, dimension(:), allocatable	allglobal::adotx
	the matrix-vector product
real, dimension(:), allocatable	allglobal::ddotx
	the matrix-vector product
real, dimension(:,:), allocatable	allglobal::solution
	this is allocated in dforce; used in mp00ac and ma02aa; and is passed to packab
real, dimension(:,:,:), allocatable	allglobal::gmreslastsolution
	used to store the last solution for restarting GMRES
real, dimension(:), allocatable	allglobal::mbpsi
	matrix vector products
logical	allglobal::liluprecond
	whether to use ILU preconditioner for GMRES
real, dimension(:,:), allocatable	allglobal::beltramiinverse
	Beltrami inverse matrix.
real, dimension(:,:,:), allocatable	allglobal::diotadxup
	measured rotational transform on inner/outer interfaces for each volume; d(transform)/dx; (see dforce)
real, dimension(:,:,:), allocatable	allglobal::ditgpdxtp
	measured toroidal and poloidal current on inner/outer interfaces for each volume; d(Itor,Gpol)/dx; (see dforce)
real, dimension(:,:,:,:), allocatable	allglobal::glambda
	save initial guesses for iterative calculation of rotational-transform
integer	allglobal::lmns
	number of independent degrees of freedom in angle transformation;
real, dimension(:,:,:), allocatable	allglobal::dlambdaout

Detailed Description

• The energy, \(W \equiv \int \! dv {\; \bf B}\cdot{\bf B}\), and helicity, \(K\equiv \int \! dv \; {\bf A}\cdot{\bf B}\), functionals may be written

  \begin{eqnarray} W & = & \frac{1}{2} \; a_i \; A_{i,j} \; a_j + a_i \; B_{i,j} \; \psi_j + \frac{1}{2} \; \psi_i \; C_{i,j} \; \psi_j \label{eq:energy_globalmatrix_global} \\ K & = & \frac{1}{2} \; a_i \; D_{i,j} \; a_j + a_i \; E_{i,j} \; \psi_j + \frac{1}{2} \; \psi_i \; F_{i,j} \; \psi_j \label{eq:helicitymatrix_global} \end{eqnarray}

  where \({\bf a} \equiv \{ {\color{red} A_{\theta,e,i,l}}, {\color{blue} A_{\zeta, e,i,l}}, {\color{Orange} A_{\theta,o,i,l}}, {\color{Cerulean}A_{\zeta ,o,i,l}}, f_{e,i}, f_{o,i} \}\) contains the independent degrees of freedom and \(\boldsymbol{\psi} \equiv \{\Delta \psi_t,\Delta \psi_p\}\).
• These are allocated and deallocated in dforce(), assigned in matrix(), and used in mp00ac() and (?) df00aa().