Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

TL;DR

This paper introduces a multiscale finite element approach for nonlinear magnetoquasistatic problems in periodic materials, utilizing magnetic induction conforming formulations and homogenization theory to efficiently model complex magnetic behaviors.

Contribution

It develops a novel multiscale formulation based on magnetic induction conforming methods and homogenization, enabling efficient simulation of nonlinear magnetic materials at multiple scales.

Findings

Validated approach on a 2D periodic magnetic composite

Effective macro-meso scale information exchange demonstrated

Potential for improved simulation of magnetic devices

Abstract

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.