Lorentz gauge eddy current formulations for multiply connected piecewise homogeneous conductors

Vector potential formulations of Maxwell's equations need to be gauged, oth erwise nodally based finite element approximations lead to an ill condition ed linear system. In this paper alternative Lorentz gauge formulations will be analysed. Particular attention will be paid to the conditions to be app lied at material interfaces, bearing in mind ease of implementation in a fi nite element code and efficiency of solution. The methods discussed are des igned to cope with the most challenging physical situations, namely, multip ly connected abutting conductors made of different materials.