Applying a Legendre collocation method based on domain decomposition to calculate underwater sound propagation in a horizontally stratified environment

TL;DR

This paper introduces a domain decomposition-based Legendre collocation method for calculating underwater sound propagation in layered environments, offering improved accuracy and speed over traditional finite difference and spectral methods.

Contribution

The paper presents a novel Legendre collocation method with domain decomposition for ocean acoustics, providing a more accurate and faster alternative to existing numerical techniques.

Findings

The proposed method achieves higher accuracy than finite difference methods.

It offers comparable accuracy to spectral methods with faster computation.

Numerical experiments validate the method's effectiveness and applicability.

Abstract

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 roughly the same accuracy as but a faster calculation speed than other types of spectral methods.