基于多级离散化的Steklov特征值问题局部缺陷校正方法

IF 1.9 3区 数学 Q2 Mathematics
Fei Xu, Liu Chen, Qiumei Huang
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引用次数: 2

摘要

针对标量二阶正定偏微分方程的Steklov特征值问题,提出了一种基于多级离散化的局部缺陷校正方法。其目的是避免求解大规模方程,特别是计算成本呈指数增长的大规模Steklov特征值问题。该算法将Steklov特征值问题转化为一系列在多网格空间序列中定义的线性边值问题和一系列在粗校正空间中的小尺度Steklov特征值问题。在此基础上,利用局部缺陷校正技术将大尺度边值问题分解为小尺度子问题。该算法避免了大规模Steklov特征值问题的求解。结果表明,本文提出的算法显著提高了求解效率。此外,我们进行了数值实验和严格的理论分析来验证我们提出的方法的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Local defect-correction method based on multilevel discretization for Steklov eigenvalue problem
In this paper, we propose a local defect-correction method for solving the Steklov eigenvalue problem arising from the scalar second order positive definite partial differential equations based on the multilevel discretization. The objective is to avoid solving large-scale equations especially the large-scale Steklov eigenvalue problem whose computational cost increases exponentially. The proposed algorithm transforms the Steklov eigenvalue problem into a series of linear boundary value problems, which are defined in a multigrid space sequence, and a series of small-scale Steklov eigenvalue problems in a coarse correction space. Furthermore, we use the local defect-correction technique to divide the large-scale boundary value problems into small-scale subproblems. Through our proposed algorithm, we avoid solving large-scale Steklov eigenvalue problems. As a result, our proposed algorithm demonstrates significantly improved the solving efficiency. Additionally, we conduct numerical experiments and a rigorous theoretical analysis to verify the effectiveness of our proposed approach.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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