A Computationally Efficient Rayleigh–Ritz Model for Heterogeneous Oceanic Waveguides Using Fourier Series of Sound Speed Profile

Abstract

The normal mode method is widely used in ocean acoustic propagation. Usually, finite difference and finite element methods are used in its solution. Recently, a method has been proposed for heterogeneous layered waveguides where the depth eigenproblem is solved using the classical Rayleigh–Ritz approximation. The method has high accuracy for low to high frequency problems. However, the matrices that appear in the eigenvalue problem for radial wavenumbers require numerical integration of the matrix elements since the sound speed and density profiles are numerically defined. In this paper, a technique is proposed to reduce the computational cost of the Rayleigh–Ritz method by expanding the sound speed profile in a Fourier series using nonlinear least square fit so that the integrals of the matrix elements can be computed in closed form. This technique is tested in a variety of problems and found to be sufficiently accurate in obtaining the radial wavenumbers as well as the transmission loss in a waveguide. The computational savings obtained by this approach is remarkable, the improvements being one or two orders of magnitude.