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A Multi-Domain Collocation Method for the Accurate Computation of Normal Modes in Open Oceanic and Atmospheric Waveguides

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The computation of acoustic normal modes in oceanic or atmospheric waveguides is a delicate task, which involves determining the complex eigenvalues and eigenvectors of a variable-coefficient Helmholtz equation. The efficiency of an algorithm to perform such a calculation relies upon the effectiveness of its root finder. When dealing with semi-infinite media, only iterative methods can be utilized. In this cases, a major difficulty is associated with the need for reasonable first guesses of the sought eigenmodes. Since a priori estimations are generally unavailable, many existing codes may in some cases fail to converge. In this paper, a novel method for the computation of acoustic normal modes, which does not require any initial guess, is proposed. It consists of four different steps: the Helmholtz equation is first rewritten exactly in terms of an offset eigenvalue; it is then discretized by a multi-domain Chebyshev collocation method, which allows handling multi-layer waveguides; the resulting eigenvalue problem is quadratic and is transformed into a generalized linear eigensystem through the so-called companion matrix method (for instance, see "Differential eigenvalue problems in which the parameter appears nonlinearly", J Comp Phys 55 (1984), by T. J. Bridges and P. J. Morris); the latter problem is finally solved by the QZ algorithm. To illustrate the capabilities of the present technique, the results of three test cases are described and discussed.
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Document Type: Research Article

Publication date: May 1, 2019

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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