微磁模拟中线性系统的高效厄米与反厄米分裂方法
Efficient Hermitian and skew-Hermitian splitting methods for linear systems in micromagnetic simulations
AI总结：
针对微磁模拟中朗道-利夫希茨方程的离散线性系统，采用HSS及其不精确变体IHSS求解，实验验证了HSS收敛性及IHSS效率对分裂参数的敏感性，两种方案收敛性能相当。
AI中文摘要：
针对朗道-利夫希茨方程，采用半隐式方法得到的离散线性系统具有以下特性：它们是系数矩阵非厄米但正定的大型稀疏系统。为高效求解这些系统，我们应用厄米/反厄米分裂（HSS）方法及其不精确变体（IHSS）。一维和三维数值实验表明，在测试的网格分辨率和阻尼参数下，HSS迭代的谱半径保持在其理论上界以下，且严格小于1。此外，理论上界与实际谱半径紧密贴合，为收敛行为提供了准确估计。IHSS结果显示其在测试案例中收敛有效，且效率对分裂参数敏感。总体而言，这两种半隐式方案表现出相当的收敛行为。
英文摘要：
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.
