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Fourier Methods for harmonic scalar waves in general waveguides
Jönköping University.
Linnaeus University, Faculty of Technology, Department of Mathematics. (Vågor och signaler)
Jönköping University.
2016 (English)In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, 21-38 p.Article in journal (Refereed) Published
Abstract [en]

A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 98, no 1, 21-38 p.
Keyword [en]
Building Block Method, Conformal mappings, Dirichlet-to-Neumann operators, Fourier series, Harmonic scalar waves, Normal surface admittance
National Category
Signal Processing
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-42904DOI: 10.1007/s10665-015-9808-8ISI: 000376643300003Scopus ID: 2-s2.0-84938152325OAI: oai:DiVA.org:lnu-42904DiVA: diva2:808461
Available from: 2015-04-28 Created: 2015-04-28 Last updated: 2017-01-11Bibliographically approved

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CiteExportLink to record
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Citation style
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  • de-DE
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  • nn-NO
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  • Other locale
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Output format
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