Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations
(2014) In Numerische Mathematik 126(3). p.413-440- Abstract
Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p-version of the finite... (More)
Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p-version of the finite element method confirm the theoretical convergence rates.
(Less)
- author
- Engström, Christian LU
- publishing date
- 2014-03
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Numerische Mathematik
- volume
- 126
- issue
- 3
- pages
- 28 pages
- publisher
- Springer
- external identifiers
-
- scopus:84893873169
- ISSN
- 0029-599X
- DOI
- 10.1007/s00211-013-0568-y
- language
- English
- LU publication?
- no
- additional info
- Funding Information: The author express gratitude to William Kolata for sending his thesis and acknowledges the support by a Marie Curie Intra-European Fellowship of the European Community; Grant No. PIEF-GA-2009-237397. Moreover, I thank Kersten Schmidt and Holger Brandsmeier for implementing the used functionality in Concepts.
- id
- 072aa6a6-c72b-42c6-8cb3-f3d21b01cf4c
- date added to LUP
- 2023-03-24 11:10:42
- date last changed
- 2023-03-24 14:11:01
@article{072aa6a6-c72b-42c6-8cb3-f3d21b01cf4c,
abstract = {{<p>Galerkin spectral approximation theory for non-self-adjoint quadratic operator polynomials with periodic coefficients is considered. The main applications are complex band structure calculations in metallic photonic crystals, periodic waveguides, and metamaterials. We show that the spectrum of the considered operator polynomials consists of isolated eigenvalues of finite multiplicity with a nonzero imaginary part. The spectral problem is equivalent to a non-compact block operator matrix and norm convergence is shown for a block operator matrix having the same generalized eigenvectors as the original operator. Convergence rates of finite element discretizations are considered and numerical experiments with the p-version of the finite element method confirm the theoretical convergence rates.</p>}},
author = {{Engström, Christian}},
issn = {{0029-599X}},
language = {{eng}},
number = {{3}},
pages = {{413--440}},
publisher = {{Springer}},
series = {{Numerische Mathematik}},
title = {{Spectral approximation of quadratic operator polynomials arising in photonic band structure calculations}},
url = {{http://dx.doi.org/10.1007/s00211-013-0568-y}},
doi = {{10.1007/s00211-013-0568-y}},
volume = {{126}},
year = {{2014}},
}