An efficient numerical method for determining trapped modes in acoustic waveguides

R. Z. Dautov

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 1, pp. 68-84

Résumé

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.

Détail

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

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