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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
ETH Zurich, Seminar for Applied Mathematics.
2009 (English)In: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 70, no 1, 231-247 p.Article in journal (Refereed) Published
Abstract [en]

We study wave propagation in periodic and frequency dependent materials when the medium in a frequency interval is characterized by a real-valued permittivity. The spectral parameter relates to the quasi momentum, which leads to spectral analysis of a quadratic operator pencil where frequency is a parameter. We show that the underlying operator has a discrete spectrum, where the eigenvalues are symmetrically placed with respect to the real and imaginary axis. Moreover, we discretize the operator pencil with finite elements and use a Krylov space method to compute eigenvalues of the resulting large sparse matrix pencil.

Place, publisher, year, edition, pages
2009. Vol. 70, no 1, 231-247 p.
Keyword [en]
periodic structure, band-gap, Bloch wave, quadratic eigenvalue, gyroscopic, operator pencil
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-51430DOI: http://dx.doi.org/10.1137/080728779OAI: oai:DiVA.org:umu-51430DiVA: diva2:481866
Available from: 2012-01-23 Created: 2012-01-23 Last updated: 2017-12-08Bibliographically approved

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