Analysis of finite-element matrices arising from discretizations of helicity functionals

This paper examines the discretized helicity functional in order to demonstrate the invariance under discrete gauge transformations and to obtain a direct physical interpretation of the finite element equations. A simple analysis then yields a rigorous comparison between the amount of work required to implement a semidirect (e.g., conjugate gradient) equation solver for unpreconditioned stiffness matrix equations associated with the helicity functional and conventional functionals.