Numerical study of the magnetic skin effect: Efficient parameterization of 2D surface‐impedance solutions for linear ferromagnetic materials

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 µr 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 the physical parameters introduced in our problem.

Special issue: The 12th International Symposium on Electric and Magnetic Fields (EMF 2021)

“…Three broad topics were covered during the 12th edition of the symposium. The first major topic considers the mathematical modeling of electromagnetic problems in view of their eventual numerical solution on computers, with contributions on quasistatic time‐domain formulations 1–3 and high‐frequency formulations 4 . The second major topic treats general methodological advances in numerical methods 5,6 .…”