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Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition

Sjöberg, Daniel LU (2005) In Multiscale Modeling & Simulation 4(3). p.760-789
Abstract
We find effective, or homogenized, material parameters for Maxwell's equations when the microscopic scale becomes small compared to the scale induced by the frequencies of the imposed currents. After defining a singular value decomposition of the non-self-adjoint partial differential operator, we expand the electromagnetic field in the modes corresponding to the singular values and show that only the smallest singular values make a significant contribution to the total field when the scale is small. The homogenized material parameters can be represented with the mean values of the singular vectors through a simple formula, which is valid for wavelengths not necessarily infinitely large compared to the unit cell.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Maxwell's equations, singular value decomposition, homogenization, Bloch waves, dispersive media
in
Multiscale Modeling & Simulation
volume
4
issue
3
pages
760 - 789
publisher
SIAM Publications
external identifiers
  • wos:000232354400003
  • scopus:33645980277
ISSN
1540-3459
DOI
10.1137/040614153
language
English
LU publication?
yes
id
4290cf6a-98bd-44a8-a9e6-7e6b83d0a55e (old id 221313)
date added to LUP
2007-08-14 15:30:33
date last changed
2017-05-21 03:39:40
@article{4290cf6a-98bd-44a8-a9e6-7e6b83d0a55e,
  abstract     = {We find effective, or homogenized, material parameters for Maxwell's equations when the microscopic scale becomes small compared to the scale induced by the frequencies of the imposed currents. After defining a singular value decomposition of the non-self-adjoint partial differential operator, we expand the electromagnetic field in the modes corresponding to the singular values and show that only the smallest singular values make a significant contribution to the total field when the scale is small. The homogenized material parameters can be represented with the mean values of the singular vectors through a simple formula, which is valid for wavelengths not necessarily infinitely large compared to the unit cell.},
  author       = {Sjöberg, Daniel},
  issn         = {1540-3459},
  keyword      = {Maxwell's equations,singular value decomposition,homogenization,Bloch waves,dispersive media},
  language     = {eng},
  number       = {3},
  pages        = {760--789},
  publisher    = {SIAM Publications},
  series       = {Multiscale Modeling & Simulation},
  title        = {Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition},
  url          = {http://dx.doi.org/10.1137/040614153},
  volume       = {4},
  year         = {2005},
}