A fast multi-layer boundary element method for direct numerical simulation of sound propagation in shallow water environments

Abstract

Direct three-dimensional (3D) numerical simulations of acoustic fields in range-dependent shallow water environments remains a challenge due to environmental complexities and large computational cost. We develop an efficient 3D boundary element method (BEM) to solve the Helmholtz equation for shallow water acoustic propagation, which utilizes a Pre-corrected Fast Fourier Transform (PFFT) approach to reduce the computational effort from O(N2∼3) to O(Nlog⁡N) where N is the total number of boundary unknowns. To account for inhomogeneous media, the method allows for arbitrary number of coupled multi-layer BEM sub-domains. With O(Nlog⁡N) efficiency and the use of massively parallel high-performance computing platforms, we are able to conduct multi-layer 3D direct numerical simulations of low-mid frequency acoustics over kilometer ranges. We perform extensive validations of the method and provide two shallow water waveguide examples benchmarked against theoretical solutions. To illustrate the efficacy and usefulness of the PFFT-BEM method, we perform 3D large-scale direct numerical simulations to assess the performance of two established canonical models: axisymmetric coupled mode model for 3D seamount; and Kirchhoff approximation and perturbation theory for 3D rough surface scattering.