Barycentric rational interpolation method of the Helmholtz equation with Irregular Domain

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-03-21 DOI:10.3846/mma.2023.16408

Miaomiao Yang, Wentao Ma, Y. Ge

引用次数: 0

Abstract

In the work, a numerical method of the 2D Helmholtz equation with meshless interpolation collocation method is developed, which is defined in arbitrary domain with irregular shape. In our numerical method, based on the Chebyshev points, the partial derivatives and the spatial variables are discretized by the barycentric rational form basis function. After that the differential equations are simplified by employing differential matrix. To verify the the accuracy, effectiveness and stability in our method, some numerical tests based on the three types of different test points are adopted. Moreover, we can also verify that present method can be applied to both variable wave number problems and high wave number problems.

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不规则区域Helmholtz方程的质心有理插值方法

本文提出了一种二维Helmholtz方程的无网格插值配点法数值解法，该方程定义在任意不规则形状区域内。在我们的数值方法中，基于切比雪夫点，偏导数和空间变量通过质心有理形式基函数离散化。然后利用微分矩阵对微分方程进行化简。为了验证该方法的准确性、有效性和稳定性，采用了基于三种不同测试点的数值试验。此外，我们还验证了该方法既适用于变波数问题，也适用于高波数问题。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.