An efficient numerical method for determining trapped modes in acoustic waveguides
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 con...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2022-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/uz-eng-phm-2022-1-4.html |
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| _version_ | 1850180077405339648 |
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| author | R.Z. Dautov |
| author_facet | R.Z. Dautov |
| author_sort | R.Z. Dautov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-dd6c88bcd5634ed19ac5f00dc17e5d1f |
| institution | OA Journals |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2022-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-dd6c88bcd5634ed19ac5f00dc17e5d1f2025-08-20T02:18:19ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982022-03-011641688410.26907/2541-7746.2022.1.68-84An efficient numerical method for determining trapped modes in acoustic waveguidesR.Z. Dautov0Kazan Federal University, Kazan, 420008 RussiaAn 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.https://kpfu.ru/uz-eng-phm-2022-1-4.htmlacoustic waveguidetrapped modediscrete and continuous spectrumfinite element methodnonlinear spectral problem |
| spellingShingle | R.Z. Dautov An efficient numerical method for determining trapped modes in acoustic waveguides Учёные записки Казанского университета: Серия Физико-математические науки acoustic waveguide trapped mode discrete and continuous spectrum finite element method nonlinear spectral problem |
| title | An efficient numerical method for determining trapped modes in acoustic waveguides |
| title_full | An efficient numerical method for determining trapped modes in acoustic waveguides |
| title_fullStr | An efficient numerical method for determining trapped modes in acoustic waveguides |
| title_full_unstemmed | An efficient numerical method for determining trapped modes in acoustic waveguides |
| title_short | An efficient numerical method for determining trapped modes in acoustic waveguides |
| title_sort | efficient numerical method for determining trapped modes in acoustic waveguides |
| topic | acoustic waveguide trapped mode discrete and continuous spectrum finite element method nonlinear spectral problem |
| url | https://kpfu.ru/uz-eng-phm-2022-1-4.html |
| work_keys_str_mv | AT rzdautov anefficientnumericalmethodfordeterminingtrappedmodesinacousticwaveguides AT rzdautov efficientnumericalmethodfordeterminingtrappedmodesinacousticwaveguides |