Efficient asymptotic models for axisymmetric eddy current problems in linear ferromagnetic materials

TL;DR

This paper develops efficient asymptotic models for axisymmetric eddy current problems in linear ferromagnetic materials, reducing computational costs while maintaining accuracy at low frequencies through a multiscale expansion approach.

Contribution

It introduces a novel multiscale asymptotic expansion method tailored for axisymmetric eddy current problems in ferromagnetic materials, enhancing computational efficiency.

Findings

Two asymptotics suffice for accurate solutions at low frequencies.

The approach reduces computational costs significantly.

Numerical validation confirms the method's accuracy.

Abstract

The problem under consideration is that of time-harmonic eddy current problems in linear ferromagnetic materials surrounded by a dielectric medium with a smooth common interface. Assuming axisymmetric geometries and orthoradial axisymmetric data, we construct an efficient multiscale expansion for the orthoradial solution that provides reduced computational costs. We investigate numerically the accuracy of the approach using an analytical procedure and infinite cylinders as well. It results that the computation of two asymptotics is sufficient to ensure accurate solutions in the case of low frequencies.