Advanced

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

Sjöberg, Daniel LU (2004) In Technical Report LUTEDX/(TEAT-7124)/1-24/(2004) TEAT-7124.
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-selfadjoint 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... (More)
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-selfadjoint 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Book/Report
publication status
published
subject
in
Technical Report LUTEDX/(TEAT-7124)/1-24/(2004)
volume
TEAT-7124
pages
24 pages
publisher
[Publisher information missing]
language
English
LU publication?
yes
id
32bdd3d0-5b61-42a8-8494-ffd639a083de (old id 530303)
date added to LUP
2007-09-12 11:56:41
date last changed
2016-07-06 17:17:01
@techreport{32bdd3d0-5b61-42a8-8494-ffd639a083de,
  abstract     = {We find effective, or homogenized, material parameters for Maxwell’s equations<br/><br>
when the microscopic scale becomes small compared to the scale induced<br/><br>
by the frequencies of the imposed currents. After defining a singular value decomposition<br/><br>
of the non-selfadjoint partial differential operator, we expand the<br/><br>
electromagnetic field in the modes corresponding to the singular values, and<br/><br>
show that only the smallest singular values make a significant contribution to<br/><br>
the total field when the scale is small. The homogenized material parameters<br/><br>
can be represented with the mean values of the singular vectors through a<br/><br>
simple formula, which is valid for wavelengths not necessarily infinitely large<br/><br>
compared to the unit cell.},
  author       = {Sjöberg, Daniel},
  institution  = {[Publisher information missing]},
  language     = {eng},
  pages        = {24},
  series       = {Technical Report LUTEDX/(TEAT-7124)/1-24/(2004)},
  title        = {Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition},
  volume       = {TEAT-7124},
  year         = {2004},
}