Geodesic
An efficient numerical method for determining trapped modes in acoustic waveguides
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 1, pp. 68-84

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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. 
@article{UZKU_2022_164_1_a3,
     author = {R. Z. Dautov},
     title = {An efficient numerical method for determining trapped modes in acoustic waveguides},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {68--84},
     publisher = {mathdoc},
     volume = {164},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2022_164_1_a3/}
}
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R. Z. Dautov. An efficient numerical method for determining trapped modes in acoustic waveguides. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 1, pp. 68-84. http://geodesic.mathdoc.fr/item/UZKU_2022_164_1_a3/