Journal of Computational Acoustics, Vol. 16, No. 1 (2008) 83–116 c  IMACS COUPLED MODE AND FINITE ELEMENT APPROXIMATIONS OF UNDERWATER SOUND PROPAGATION PROBLEMS IN GENERAL STRATIFIED ENVIRONMENTS G. A. ATHANASSOULIS ∗ and K. A. BELIBASSAKIS Department of Naval Architecture and Marine Engineering National Technical University of Athens 15710 Zografos, Greece ∗ mathan@central.ntua.gr D. A. MITSOUDIS †,‡ , N. A. KAMPANIS † and V. A. DOUGALIS †,§,¶ † Institute of Applied and Computational Mathematics F.O.R.T.H., P.O. Box 1527, 71110 Heraklion, Greece doug@math.uoa.gr ‡ Department of Applied Mathematics, University of Crete 71409 Heraklion, Greece § Department of Mathematics, University of Athens, 15784 Zographou, Greece Received 15 November 2004 Revised 9 May 2005 We compare the results of a coupled mode method with those of a finite element method and also of COUPLE on two test problems of sound propagation and scattering in cylindrically symmetric, underwater, multilayered acoustic waveguides with range-dependent interface topographies. We observe, in general, very good agreement between the results of the three codes. In some cases in which the frequency of the harmonic point source is such that an eigenvalue of the local vertical problem remains small in magnitude and changes sign several times in the vicinity of the interface nonhomogeneity, the discrepancies between the results of the three codes increase, but remain small in absolute terms. Keywords : Underwater acoustics; range-dependent waveguides; comparison of coupled mode and finite element codes. 1. Introduction Solving numerically the sound propagation and scattering problem in range-dependent marine waveguides is a task of central importance in underwater acoustics. In this paper, we consider a cylindrically symmetric environment consisting in part of a water layer overlying ¶ Corresponding author. 83