Modeling three-dimensional acoustic propagation in underwater waveguides using the longitudinally invariant finite element method

Three-dimensional acoustic propagation in shallow water waveguides is studied using the longitudinally invariant finite element method. This technique is appropriate for environments with lateral variations that occur in only one dimension. In this method, a transform is applied to the three-dimensional Helmholtz equation to remove the range-independent dimension. The finite element method is employed to solve the transformed Helmholtz equation for each out-of-plane wavenumber. Finally, the inverse transform is used to transform the pressure field back to three-dimensional spatial coordinates. Due to the oscillatory nature of the inverse transform, two integration techniques are developed. The first is a Riemann sum combined with a wavenumber sampling method that efficiently captures the essential components of the integrand. The other is a modified adaptive Clenshaw-Curtis quadrature. Three-dimensional transmission loss is computed for a Pekeris waveguide, underwater wedge, and Gaussian canyon. For each waveguide, the two integration schemes are compared in terms of accuracy and efficiency.