Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

2022/10/26 by Lin, Zhuonan, Lomakin, Vitaliy
#Applied Physics (physics.app-ph) #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)

paper · doi:10.48550/arxiv.2210.14525

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.

Related

• BDF2-type integrator for Landau-Lifshitz-Gilbert equation in micromagnetics, part I: unconditional weak convergence to weak solutions
• Solutions to the Landau-Lifshitz-Gilbert equation in the frequency space: Discretization schemes for the dynamic-matrix approach
• Numerical analysis of the Landau-Lifshitz-Gilbert equation with inertial effects
• A convergent finite element approximation for the quasi-static Maxwell--Landau--Lifshitz--Gilbert equations
• A decoupled, convergent and fully linear algorithm for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects