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Complex dispersion relation calculations with the symmetric interior penalty method

Engström, C. LU and Wang, M. LU (2010) In International Journal for Numerical Methods in Engineering 84(7). p.849-863
Abstract

A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivity and we relate for this absorptive system the spectral parameter to the time frequency. We transform the non-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problem and uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact of the penalty term numerically and illustrate the high convergence rate of the method.

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author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Absorptive, Bandstructure, Discontinuous Galerkin method, Non-linear eigenvalue problem, Photonic crystal
in
International Journal for Numerical Methods in Engineering
volume
84
issue
7
pages
15 pages
publisher
John Wiley & Sons Inc.
external identifiers
  • scopus:78049303077
ISSN
0029-5981
DOI
10.1002/nme.2926
language
English
LU publication?
no
id
df9d305e-5801-46d1-8f81-b407821c7114
date added to LUP
2023-03-24 11:15:50
date last changed
2023-03-24 15:07:03
@article{df9d305e-5801-46d1-8f81-b407821c7114,
  abstract     = {{<p>A high-order discontinuous Galerkin method for calculations of complex dispersion relations of two-dimensional photonic crystals is presented. The medium is characterized by a complex-valued permittivity and we relate for this absorptive system the spectral parameter to the time frequency. We transform the non-linear eigenvalue problem for a Lorentz material in air into a non-Hermitian linear eigenvalue problem and uses a Krylov space method to compute approximate eigenvalues. Moreover, we study the impact of the penalty term numerically and illustrate the high convergence rate of the method.</p>}},
  author       = {{Engström, C. and Wang, M.}},
  issn         = {{0029-5981}},
  keywords     = {{Absorptive; Bandstructure; Discontinuous Galerkin method; Non-linear eigenvalue problem; Photonic crystal}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{849--863}},
  publisher    = {{John Wiley & Sons Inc.}},
  series       = {{International Journal for Numerical Methods in Engineering}},
  title        = {{Complex dispersion relation calculations with the symmetric interior penalty method}},
  url          = {{http://dx.doi.org/10.1002/nme.2926}},
  doi          = {{10.1002/nme.2926}},
  volume       = {{84}},
  year         = {{2010}},
}