三乘三块鞍点问题的新块三角形预处理器

Pub Date : 2023-12-07 DOI:10.21136/AM.2023.0289-22

Jun Li, Xiangtuan Xiong

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引用次数: 0

摘要

本文针对三乘三块鞍点问题，建立了一种新的块三角形（NBT）预条件器，它能有效避免将块预条件器应用于克雷洛夫子空间方法时，线性子系统系数矩阵为舒尔补码矩阵的求解难题。理论分析表明，NBT 预处理器产生的迭代方法是无条件收敛的。此外，还讨论了一些光谱特性。最后，通过数值实验证明了 NBT 预处理的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A new block triangular preconditioner for three-by-three block saddle-point problem

In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.

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