Abstract

In this article, we propose an optimization method for a difference scheme for the numerical solution of the Helmholtz equation, applicable for any ratio of the grid steps. In the range of the number of points per wavelength of practical interest, the dispersion error of the optimal scheme is comparable with the error of higher order schemes known in the literature.

中文翻译：

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亥姆霍兹方程数值解的有限差分格式的优化

摘要

在本文中，我们为Helmholtz方程的数值解决方案的差分方案提出了一种优化方法，该方法适用于任何比例的网格步长。在实际感兴趣的每个波长的点数范围内，最佳方案的色散误差与文献中已知的高阶方案的误差相当。