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A three-dimensional, longitudinally-invariant finite element (FE) model for shallow water acoustic propagation is constructed through a cosine transform of a series of two-dimensional FE models at different values of the out-of-plane wavenumber. An innovative wavenumber sampling method is developed that efficiently captures the essential components of the integral as the out-of-plane wave number approaches the water wavenumber. The method is validated by comparison with benchmark solutions of two shallow water waveguide environments: a flat range independent case and a benchmark wedge.


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