arXiv subjects

Yingxi Miao

Publications and source records attributed to Yingxi Miao.

3 recordsLinked to original sources

arXiv2026

Efficient Hermitian and skew-Hermitian splitting methods for linear systems in micromagnetic simulations

For the Landau-Lifshitz equation, the discrete linear systems obtained by our semi-implicit method possess the following properties: they are large-sparse systems with non-Hermitian yet positive-definite coefficient matrices. To solve these systems efficiently, we apply the Hermitian/skew-Hermitian splitting (HSS) method and its inexact variant (IHSS). Numerical experiments in one and three dimensions show that the spectral radius of the HSS iteration remains below its theoretical upper bound and strictly below one for the tested grid resolutions and damping parameters. Moreover, the theoretical bound closely follows the actual spectral radius, providing an accurate estimate of the convergence behavior. The IHSS results demonstrate effective convergence for the tested cases and show that its efficiency is sensitive to the splitting parameter. Overall, the two semi-implicit schemes exhibit comparable convergence behavior.

math.NA↗

arXiv2026

Improved Energy Stable Symmetric Gauss-Seidel Projection Method for Micromagnetics Simulations

The Gauss-Seidel projection method (GSPM) constitutes an efficient and numerically stable numerical framework for micromagnetic simulations of ferromagnetic media. This scheme attains first-order temporal accuracy and second-order spatial accuracy. Fast Fourier transform (FFT) techniques can be incorporated to accelerate both the solution of the arising linear algebraic systems and the evaluation of stray magnetic fields. The conventional GSPM relies on a single-sided Gauss-Seidel iteration, which leverages the latest updated state variables associated with the heat-diffusion subproblem. In this work, we develop a symmetric Gauss-Seidel projection method (SGSPM) that retains first-order temporal accuracy and second-order spatial consistency. The proposed symmetric variant exhibits superior stability properties relative to the standard GSPM. Specifically, SGSPM adopts a two-pass symmetric Gauss-Seidel iteration, where updated information from the heat-diffusion stage is fully exploited to rigorously guarantee discrete energy stability. We validate the performance of the devised scheme through numerical investigations of magnetization dynamic evolution and magnetic domain-wall propagation. Numerical evidence demonstrates that the improved symmetric scheme delivers enhanced stability for capturing magnetization motion dynamics.

math.NA↗

arXiv2026

An Efficient Energy Stable Structure Preserving Method for The Landau-Lifshitz Equation

One of the main difficulties in micromagnetics simulation is the norm preserving constraints $\|\mathbf{m}\|=1$ at the continuous or the discrete level. Another difficulty is the stability with the time step constraint. Using standard explicit integrators leads to a physical time step of sub-pico seconds, which is often two orders of magnitude smaller than the fastest physical time scales. Direct implicit integrators require solving complicated, coupled systems. Another major difficulty with the projection method in this field is the lack of rigorous theoretical guarantees regarding its stability of the projection step. In this paper, we introduce a first order method. Such a method is structure preserving based on a combination of a Gauss-Seidel iteration, a double diffusion iteration and a Crank-Nicolson iteration to preserve the norm constraints.

math.NA↗