标题： 双鞍点问题的一种新的正则化预条件子类 显示英文标题

标题： A new class of regularized preconditioners for double saddle-point problems

摘要： 双鞍点问题的块结构引发了对高效预条件器的广泛研究。 本文介绍了一类新型的三乘三块预条件器，专门针对来自时变麦克斯韦方程或液晶取向建模的此类系统。 本工作的主要动机是突出最近的预条件器在高雷诺数下的局限性，因为原始研究未探讨此情形，并证明我们的预条件器在这些情况下优于现有的预条件器。 我们全面分析了所提出的预条件器的收敛性和谱性质。 我们展示了所提出的预条件器的效率，并验证了理论界限。 显示英文摘要

摘要： The block structure of double saddle-point problems has prompted extensive research into efficient preconditioners. This paper introduces a novel class of three-by-three block preconditioners tailored for such systems from the time-dependent Maxwell equations or liquid crystal director modeling. The main motivation of this work is to highlight the limitations of recent preconditioners under high Reynolds numbers, as the original studies did not explore this scenario, and to demonstrate that our preconditioner outperforms the existing ones in such regimes. We thoroughly analyze the convergence and spectral properties of the proposed preocnditioner. We illustrate the efficiency of the proposed preconditioners, and verify the theoretical bounds.