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Homogenization of the Maxwell Equations at Fixed Frequency

Wellander, Niklas LU and Kristensson, Gerhard LU (2003) In SIAM Journal on Applied Mathematics 64(1). p.170-195
Abstract
The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calderón operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result... (More)
The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calderón operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result on the correctors. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Applied Mathematics
volume
64
issue
1
pages
170 - 195
publisher
SIAM Publications
external identifiers
  • wos:000187741700009
  • scopus:1842458239
ISSN
0036-1399
DOI
language
English
LU publication?
yes
id
2ba4d526-3442-46ff-8caa-92c0716c2d91 (old id 144266)
date added to LUP
2007-07-11 09:49:36
date last changed
2018-05-29 11:06:01
@article{2ba4d526-3442-46ff-8caa-92c0716c2d91,
  abstract     = {The homogenization of the Maxwell equations at fixed frequency is addressed in this paper. The bulk (homogenized) electric and magnetic properties of a material with a periodic microstructure are found from the solution of a local problem on the unit cell by suitable averages. The material can be anisotropic and satisfies a coercivity condition. The exciting field is generated by an incident field from sources outside the material under investigation. A suitable sesquilinear form is defined for the interior problem, and the exterior Calderón operator is used to solve the exterior radiating fields. The concept of two-scale convergence is employed to solve the homogenization problem. A new a priori estimate is proved as well as a new result on the correctors.},
  author       = {Wellander, Niklas and Kristensson, Gerhard},
  issn         = {0036-1399},
  language     = {eng},
  number       = {1},
  pages        = {170--195},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Applied Mathematics},
  title        = {Homogenization of the Maxwell Equations at Fixed Frequency},
  url          = {http://dx.doi.org/},
  volume       = {64},
  year         = {2003},
}