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

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.