Applying a Chebyshev collocation method based on domain decomposition for calculating underwater sound propagation in a horizontally stratified environment.

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.