FEM-BEM Coupling with Ferromagnetic Materials

Eddy current problems are typically modelled by a combination of Ampère’s law, Ohm’s law, the non-existence of magnetic monopoles and Faraday’s law of induction. Using a magnetic vector potential A, such that the magnetic flux intensity is given by B = curl A, we end up with the equation σ ∂ t A + curl ν(A) curl A = Js [1]. Here, Js are applied source currents, ν(A) the magnetic reluctivity whose dependence on A implies the possible non-linearity of the material behaviour, and σ is the electrical conductivity. In most applications, the domain of interest consists of conducting (e.g. metal parts) and non-conducting regions (e.g. air). In the non-conducting regions, the part σ ∂ tA is dropped from the equation and the model is that of magnetostatics.