A Chebyshev collocation method for directly solving two-dimensional ocean acoustic propagation in linearly varying seabed.

The article focuses on a novel collocation spectral method developed for directly solving the two-dimensional Helmholtz equation governing ocean acoustic propagation in irregular domains, including those with linearly varying seabeds and inhomogeneous fluid conditions. This method extends traditional spectral techniques beyond rectangular domains by employing a unique point selection strategy based on concentric curves within the solution region, enabling high-precision calculations without relying on simplified acoustic models. Numerical examples demonstrate that the spectral method achieves significantly higher accuracy and faster convergence than established programs like Kraken and COUPLE, particularly in scenarios involving variable acoustic speed and density. While the method currently excels for linear seabed variations and low-frequency sources, challenges remain in handling complex terrains and improving computational efficiency, with future work aimed at three-dimensional extensions and acceleration techniques. This approach offers a promising, generalizable computational tool for underwater acoustic applications relevant to marine exploration, target detection, and fisheries.