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On two numerical methods for homogenization of Maxwell's equations

Engström, Christian LU and Sjöberg, Daniel LU orcid (2007) In Journal Electromagnetic Waves and Applications 21(13). p.1845-1856
Abstract
When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Journal Electromagnetic Waves and Applications
volume
21
issue
13
pages
1845 - 1856
publisher
VSP BV
external identifiers
  • wos:000250206800010
  • scopus:34547303103
ISSN
1569-3937
DOI
10.1163/156939307781891076
language
English
LU publication?
yes
id
46c43c4d-fe23-4f16-a89e-e424c291d6b3 (old id 637534)
date added to LUP
2016-04-01 11:48:52
date last changed
2023-06-24 04:00:08
@article{46c43c4d-fe23-4f16-a89e-e424c291d6b3,
  abstract     = {{When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.}},
  author       = {{Engström, Christian and Sjöberg, Daniel}},
  issn         = {{1569-3937}},
  language     = {{eng}},
  number       = {{13}},
  pages        = {{1845--1856}},
  publisher    = {{VSP BV}},
  series       = {{Journal Electromagnetic Waves and Applications}},
  title        = {{On two numerical methods for homogenization of Maxwell's equations}},
  url          = {{http://dx.doi.org/10.1163/156939307781891076}},
  doi          = {{10.1163/156939307781891076}},
  volume       = {{21}},
  year         = {{2007}},
}