On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials
(2009) In SIAM Journal on Applied Mathematics 70(1). p.231-247- Abstract
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.
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https://lup.lub.lu.se/record/2103ac2f-1d03-4d34-ae98-e038551b7765
- author
- Engstr̈om, Christian LU and Richter, Markus
- publishing date
- 2009
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Band-gap, Bloch wave, Gyroscopic, Operator pencil, Periodic structure, Quadratic eigenvalue
- in
- SIAM Journal on Applied Mathematics
- volume
- 70
- issue
- 1
- pages
- 17 pages
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- scopus:67649352502
- ISSN
- 0036-1399
- DOI
- 10.1137/080728779
- language
- English
- LU publication?
- no
- id
- 2103ac2f-1d03-4d34-ae98-e038551b7765
- date added to LUP
- 2023-03-24 11:27:22
- date last changed
- 2023-03-24 15:17:48
@article{2103ac2f-1d03-4d34-ae98-e038551b7765, abstract = {{<p>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.</p>}}, author = {{Engstr̈om, Christian and Richter, Markus}}, issn = {{0036-1399}}, keywords = {{Band-gap; Bloch wave; Gyroscopic; Operator pencil; Periodic structure; Quadratic eigenvalue}}, language = {{eng}}, number = {{1}}, pages = {{231--247}}, publisher = {{Society for Industrial and Applied Mathematics}}, series = {{SIAM Journal on Applied Mathematics}}, title = {{On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials}}, url = {{http://dx.doi.org/10.1137/080728779}}, doi = {{10.1137/080728779}}, volume = {{70}}, year = {{2009}}, }