Abstract The inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GMRES it requires much smaller workspace while may converge considerably faster than BiCGStab. The effectiveness of the proposed methods is illustrated with matrix pencils of order up to 3.1 ⋅ 106 arising in the temporal linear stability analysis of a typical hydrodinamic flow.

中文翻译：

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求解流体动力学时间稳定性分析中出现的特征问题的非精确牛顿法

摘要 较早开发的用于计算与规则线性大稀疏非厄米矩阵柱的有限特征值的分离组相关联的收缩子空间的不精确牛顿方法专门用于解决流体动力学时间稳定性分析中出现的特征问题。为此，针对在牛顿法每一步求解的线性系统，提出了一种基于多级二阶不完全LU分解的新型高效MLILU2预处理器。开发了具有正确预处理的 Krylov 子空间方法 IDR2 的特殊变体。与 GMRES 相比，它需要的工作空间小得多，但收敛速度可能比 BiCGStab 快得多。所提出方法的有效性用阶数高达 3 的矩阵铅笔来说明。