Lorentz gauge formulations for eddy current problems involving piecewise homogeneous conductors

It is well known that vector potential formulations of Maxwell´s equations need to be gauged, otherwise a nodally based finite element approximation 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 be paid to material interface conditions, and the ease of implementation in a finite element code. The goal is to arrive at an efficient system, capable of solving multiply connected, abutting conductors, made of different materials