On a decoupled linear FEM integrator for Eddy-current-LLG

TL;DR

This paper introduces a decoupled linear finite element method for simulating the coupled eddy-current and Landau-Lifshitz-Gilbert equations, requiring only linear solves per step and proving convergence.

Contribution

It presents a novel decoupled linear FEM integrator for the coupled eddy-current and LLG equations, with proven convergence and efficient linear solves.

Findings

Algorithm requires only two linear solves per time-step.

Unconditional convergence to a weak solution is established.

Numerical experiments demonstrate the method's effectiveness.

Abstract

We propose a numerical integrator for the coupled system of the eddy-current equation with the nonlinear Landau-Lifshitz-Gilbert equation. The considered effective field contains a general field contribution, and we particularly cover exchange, anisotropy, applied field, and magnetic field (stemming from the eddy-current equation). Even though the considered problem is nonlinear, our scheme requires only the solution of two linear systems per time-step. Moreover, our algorithm decouples both equations so that in each time-step, one linear system is solved for the magnetization, and afterwards one linear system is solved for the magnetic field. Unconditional convergence -- at least of a subsequence -- towards a weak solution is proved, and our analysis even provides existence of such weak solutions. Numerical experiments with a micromagnetic benchmark problem underline the performance of the proposed algorithm.