Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials
Dima Abou El Nasser El Yafi, Victor Hugo Santiago Peron, Ronan Perrussel, Laurent Krähenbühl · International Journal of Numerical Modelling Electronic Networks Devices and Fields · 2022
Abstract This work presents an efficient method based on asymptotic models in order to solve numerically eddy current problems in a bi‐dimensional setting with a high contrast of linear relative magnetic permeability μ r ≫ 1 between a conductor and a dielectric subdomain. We describe a magnetic skin effect by deriving a multiscale expansion for the magnetic potential in power series of a small parameter δ which represents the skin depth. We make explicit the first asymptotics up to the order three. Some numerical results based on the finite element method will be presented to illustrate the magnetic skin effect and to validate the performance of the proposed asymptotic models in the dielectric medium. We confirm that the proposed asymptotics provide reduced computational costs for a wide range of physical parameters introduced in our problem.