An efficient numerical method for determining trapped modes in acoustic waveguides

R.Z. Dautov

Kazan Federal University, Kazan, 420008 Russia

E-mail:  rafail.dautov@gmail.com

Received February 1, 2022


ORIGINAL ARTICLE

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DOI: 10.26907/2541-7746.2022.1.68-84

For citation: Dautov R.Z. An efficient numerical method for determining trapped modes in acoustic waveguides. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie  Nauki,  2022,  vol.  164,  no.  1,  pp.  68–84.  doi:  10.26907/2541-7746.2022.1.68-84. (In Russian)

Abstract

An efficient numerical method for determining all trapped modes of the Helmholtz equation based on the finite element method and exact nonlocal boundary conditions is proposed. An infinite two-dimensional channel with parallel walls at infinity, which may contain obstacles of arbitrary shape, is considered. It is assumed that the frequencies of the trapped modes lie below a certain threshold value. The discrete problem is an algebraic eigenvalue problem for symmetric positive definite sparse matrices, one of which depends nonlinearly on the spectral parameter. A fast iterative method for solving such problems is introduced. The results of the numerical calculations are presented.

Keywords: acoustic waveguide, trapped mode, discrete and continuous spectrum, finite element method, nonlinear spectral problem

Acknowledgments. This study was supported by the Kazan Federal University Strategic Academic Leadership Program (“PRIORITY-2030”).

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