AI 中文总结
本文针对液晶指向矢建模的双鞍点系统，提出双参数块预条件子，建立收敛条件、完成谱分析以确定参数策略，用于加速柔性GMRES收敛，实验验证其性能优异。
AI 中文摘要
本文针对液晶指向矢建模有限元离散得到的一类双鞍点系统，提出一种新型块预条件子。首先建立保证基础迭代格式收敛的充分条件，随后对预条件矩阵进行谱分析，得到有效的参数选取策略。该预条件子用于加速柔性GMRES的收敛，实验结果证实该方法性能优异。
英文摘要
This paper introduces a novel block preconditioner for a class of double saddle point systems arising from the finite element discretization of liquid crystal director modeling. We first establish sufficient conditions to guarantee the convergence of the underlying iterative scheme. A spectral analysis of the preconditioned matrix is then performed, leading to an effective strategy for parameter selection. The new preconditioner is used to accelerate the convergence of the flexible version of GMRES. Experimental results confirm the strong performance of the method.
Comments21 pages, 4 tables, 4 figures, submitted
