Helmholtz方程Steklov特征值问题的快速小波配置压缩方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-03-10 DOI:10.1016/j.aml.2025.109532

Guangqing Long , Huanfeng Yang , Li-Bin Liu

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引用次数: 0

摘要

针对Steklov特征值问题，提出了一种基于压缩技术的快速小波配置方法。基于势理论，将Steklov特征值问题重新表述为具有对数奇异性的边界积分方程。利用压缩技术，将小波系数矩阵截断为稀疏矩阵。这种技术使算法更快。结果表明，该方法只需要线性计算复杂度，并且对近似特征值和特征函数具有最优收敛阶。给出了数值算例并进行了分析。

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A fast wavelet collocation method with compression techniques for Steklov eigenvalue problems of Helmholtz equations

A fast wavelet collocation method with compression techniques is proposed for solving the Steklov eigenvalue problem. Based on the potential theory, the Steklov eigenvalue problem is reformulated as a boundary integral equation with logarithmic singularity. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique leads to the algorithm faster. We show that the proposed method requires only linear computational complexity and has the optimal convergence order for the approximate eigenvalues and eigenfunctions. The numerical examples are provided and analyzed.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.