A novel third-order accurate and stable scheme for micromagnetic simulations

TL;DR

This paper introduces a new third-order accurate and stable numerical scheme for simulating magnetization dynamics in micromagnetics, improving accuracy and efficiency over existing methods while maintaining stability across various damping coefficients.

Contribution

The paper presents a novel third-order temporally accurate scheme for the LLG equation that enhances computational efficiency and stability compared to existing methods.

Findings

Achieves strict third-order temporal accuracy.

Offers superior computational efficiency and convergence.

Produces magnetic microstructures in excellent agreement with benchmarks.

Abstract

High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and stable numerical scheme for the Landau-Lifshitz-Gilbert (LLG) equation, aiming to address the limitations in accuracy and efficiency often encountered with conventional approaches. Validation via nanostrip simulations confirms two principal advantages of the proposed method: it attains strict third-order temporal accuracy, surpassing many current techniques, and it offers superior computational efficiency, enabling rapid convergence without sacrificing numerical precision. For Gilbert damping coefficients $\alpha$ ranging from $0.1$ to values below $10$, the scheme preserves strong stability and effectively avoids non-physical magnetization states. The magnetic microstructures predicted by this method are in excellent agreement with those from established benchmark methods, affirming its reliability for quantitative physical analysis. Salient distinctions between the proposed scheme and an existing third-order semi-implicit method include: (1) Solving the linear system associated with the existing scheme demands substantially greater computational time, underscoring the need for highly efficient solvers; (2) Although the proposed method shows increased sensitivity to damping parameters, it reliably converges to stable physical states and is effective in simulating magnetic domain wall motion, producing outcomes consistent with prior validated studies; (3) The energy levels computed by the proposed method are significantly lower than those obtained via the existing third-order scheme.