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On the spectrum of an operator pencil with applications to wave propagation in periodic and frequency dependent materials

Engstr̈om, Christian LU and Richter, Markus (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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author
and
publishing date
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}},
}