It is well known that vector potential formulations of Maxwell's equat
ions need to be gauged, otherwise a nodally based finite element appro
ximation leads to an ill conditioned matrix system. This paper studies
alternative Lorentz gauge formulations, since they have the potential
for providing highly efficient solutions, Particular attention will b
e paid to material interface conditions, and the ease of implementatio
n in a finite element code. The goal is to arrive at an efficient syst
em, capable of solving multiply connected, abutting conductors, made o
f different materials.