山东师范大学学报(自然科学版)

2019, v.34;No.148(04) 408-415

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一维Helmholtz方程的优化差分法
AN OPTIMAL FINITE DIFFERENCE SCHEME FOR THE ONE-DIMENSIONAL HELMHOLTZ EQUATION

周鲁川;吴亭亭;
Zhou Luchuan;Wu Tingting;School of Mathematics and Statistics, Shandong Normal University;

摘要(Abstract):

对一维Helmholtz方程建立了优化的二阶差分格式.对数值波数和真实波数之间的误差进行了分析.基于极小化数值频散的思想,提出了选取加权系数的整体选取法和加细选取法.数值实验表明带加细参数的差分格式提高了数值精度,有效地抑制了数值频散.
This paper presents an optimized second-order difference scheme for the one-dimensional Helmholtz equation. We analyze the error between the numerical wavenumber and the real wavenumber. Based on the idea of minimizing numerical dispersion, a global choice strategy and a refined choice strategy are proposed for selecting weighting coefficients of the difference scheme. Numerical experiments indicate that the difference method with the refined parameters improves the numerical accuracy and suppresses the numerical dispersion efficiently.

关键词(KeyWords): Helmholtz方程;差分格式;数值频散
Helmholtz equation;finite difference schemes;numerical dispersion

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基金项目(Foundation): 国家自然科学基金资助项目(11301310);; 山东省高等学校科学技术计划资助项目(J18KA221);; 山东师范大学大学生创新创业训练计划资助项目(201810445356)

作者(Author): 周鲁川;吴亭亭;
Zhou Luchuan;Wu Tingting;School of Mathematics and Statistics, Shandong Normal University;

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