Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

TL;DR

This paper introduces a finite element solver for the linearized Landau-Lifshitz-Gilbert equation in the frequency domain, enabling efficient analysis of magnetic systems under weak harmonic excitation.

Contribution

It presents a novel finite element method for linearized LLGE in the frequency domain, including a preconditioner and iterative solver for improved efficiency.

Findings

Solver demonstrates validity and effectiveness through numerical examples.

Achieves fast and scalable solutions for magnetic systems.

Provides a new tool for frequency domain analysis of magnetization dynamics.

Abstract

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.