A modal approach for the solution of the non-linear induction problem in ferromagnetic media

TL;DR

This paper introduces a fast, mesh-free modal approach using fixed-point iteration for solving non-linear induction problems in ferromagnetic media, applicable to harmonic and pulse excitations.

Contribution

It presents a novel modal method combined with fixed-point iteration that avoids domain meshing, enabling faster computations for non-linear magnetic problems.

Findings

Efficient solution for 1D non-linear induction problems

Fast inverse Laplace transform using GPOF method

Potential extension to 2D and 3D problems

Abstract

The non-linear induction problem in ferromagnetic media is solved using the fixed-point iteration method, where the linearized problem at each iteration is treated by means of a modal approach. The proposed approach does not require meshing of the solution domain, which results in fast computations comparing to conventional mesh-based numerical techniques. Both harmonic and pulse excitations are considered via Fourier and Laplace transform, respectively. An efficient method for the fast computation of the inverse Laplace transform of the magnetic polarization signals is also devised based on the generalized pencil-of-function (GPOF) method. Although being restricted to one dimensional configurations, the present work provide the tools for the treatment of two and three dimensional problems, whose study is under way.