The propagation of sound waves in a horizontally stratified environment, a classical problem in ocean acoustics, has traditionally been calculated using normal modes. Most programs based on the normal mode model are discretized using the finite difference method (FDM). This paper proposes a Chebyshev collocation method (CCM) based on domain decomposition to solve this problem. A set of collocation points cannot penetrate two layers of media, thus necessitating domain decomposition and the use of two sets of collocation points. The solution process of this method proceeds entirely in physical space, requiring that the original differential equation be strictly established at the collocation points; thus, a dense matrix eigenvalue problem is formed, from which the solution for the horizontal wavenumbers and modes can be directly obtained. Numerical experiments are presented to demonstrate the validity and applicability of this method. A comparison with other methods shows that the CCM proposed in this article is slightly slower but more accurate than the FDM, while it offers roughly the same accuracy but a faster speed than other types of spectral methods.

中文翻译：

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应用基于域分解的切比雪夫搭配方法计算水平分层环境中的水声传播

声波在水平分层环境中的传播是海洋声学中的一个经典问题，传统上是使用法向模式计算的。大多数基于正常模式模型的程序都使用有限差分法 (FDM) 进行离散化。本文提出了一种基于域分解的切比雪夫搭配方法（CCM）来解决这个问题。一组搭配点不能穿透两层媒体，因此需要域分解和使用两组搭配点。该方法的求解过程完全在物理空间中进行，要求原始微分方程在配置点上严格建立；这样就形成了一个稠密矩阵特征值问题，由此可以直接得到水平波数和模式的解。数值实验证明了该方法的有效性和适用性。与其他方法的比较表明，本文提出的 CCM 比 FDM 稍慢但精度更高，而它提供的精度与其他类型的频谱方法大致相同，但速度更快。