The propagation of sound waves in a horizontally stratified environment, a classic 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). In this paper, a Legendre collocation method (LCM) based on domain decomposition is proposed to solve this problem. A set of collocation points cannot penetrate multiple layers of media, thus necessitating domain decomposition and the use of multiple 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 system 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 LCM proposed in this article is more accurate than the FDM and offers approximately the same accuracy as, but a faster calculation speed than, other types of spectral methods.

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，传统上一直使用法向模式进行计算。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勒让德搭配方法（LCM）来解决这个问题。一组搭配点不能穿透多层媒体，因此需要域分解和使用多组搭配点。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；因此，形成了一个稠密矩阵特征值系统，从中可以直接获得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 LCM 比 FDM 更准确，并且提供与其他类型的光谱方法大致相同的精度，但计算速度更快。