A comparison between current-based integral equations approaches for eddy current problems

Abstract

Abstract In this paper, a comparison between two current-based Integral Equations approaches for eddy current problems is presented. In particular, the very well-known and widely adopted loop-current formulation (or electric vector potential formulation) is compared to the less common J-φ formulation. Pros and cons of the two formulations with respect to the problem size are discussed, as well as the adoption of low-rank approximation techniques. Although rarely considered in the literature, it is shown that the J-φ formulation may offer some useful advantages when large problems are considered. Indeed, for large-scale problems, while the computational efforts required by the two formulations are comparable, the J-φ formulation does not require any particular attention when non-simply connected domains are considered.