Fourier beyond dispersion: Wavenumber explicit and precise accuracy of FDMs for the Helmholtz equation

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-04-15 DOI:10.1016/j.aml.2025.109576

Hui Zhang

引用次数: 0

Abstract

We propose a practical tool for evaluating and comparing the accuracy of FDMs for the Helmholtz equation. The tool based on Fourier analysis makes it easy to find wavenumber explicit order of convergence, and can be used for rigorous proof. It fills in the gap between the dispersion analysis and the actual error with source term. We illustrate it for classical and some dispersion free schemes in 1D, with conclusions verified by numerical experiments.

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傅里叶超越色散：亥姆霍兹方程fdm的波数显式和精确精度

我们提出了一个实用的工具来评估和比较fdm对亥姆霍兹方程的精度。基于傅里叶分析的工具可以很容易地找到波数的显式收敛阶，并且可以用于严格的证明。它用源项填补了色散分析与实际误差之间的空白。我们对一维的经典格式和一些无色散格式进行了说明，并通过数值实验验证了结论。

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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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.