On the vector potential formulation with an energy-based hysteresis model and its numerical solution

TL;DR

This paper integrates an energy-based hysteresis model into vector potential formulations for magnetic field equations, enabling accurate simulation of ferromagnetic devices with proven solution existence, uniqueness, and efficient numerical methods.

Contribution

It introduces a systematic approach to incorporate an energy-based hysteresis model into vector potential formulations, with proven mathematical properties and globally convergent iterative solution methods.

Findings

Established existence and uniqueness of solutions.

Developed two globally convergent iterative methods.

Demonstrated efficiency through numerical benchmark tests.

Abstract

The accurate modelling and simulation of electric devices involving ferromagnetic materials requires the appropriate consideration of magnetic hysteresis. We discuss the systematic incorporation of the energy-based vector hysteresis model of Henrotte et al. into vector potential formulations for the governing magnetic field equations. The field model describing a single step in a load cycle is phrased as a convex minimization problem which allows us to establish existence and uniqueness of solutions and to obtain accurate approximations by finite element discretization. Consistency of the model with the governing field equations is deduced from the first order optimality conditions. In addition, two globally convergent iterative methods are presented for the solution of the underlying minimization problems. The efficiency of the approach is illustrated by numerical tests for a typical benchmark problem.