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)
- 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:
https://lup.lub.lu.se/record/530303
- author
- Sjöberg, Daniel
LU
- organization
- publishing date
- 2004
- type
- Book/Report
- publication status
- published
- subject
- in
- Technical Report LUTEDX/(TEAT-7124)/1-24/(2004)
- pages
- 24 pages
- publisher
- [Publisher information missing]
- report number
- TEAT-7124
- language
- English
- LU publication?
- yes
- additional info
- Published version: Multiscale Modeling & Simulation, Vol. 4, No. 3, pp. 760-789, 2005.
- id
- 32bdd3d0-5b61-42a8-8494-ffd639a083de (old id 530303)
- date added to LUP
- 2016-04-04 13:16:24
- date last changed
- 2018-11-21 21:12:58
@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}},
number = {{TEAT-7124}},
series = {{Technical Report LUTEDX/(TEAT-7124)/1-24/(2004)}},
title = {{Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition}},
url = {{https://lup.lub.lu.se/search/files/6082002/624870.pdf}},
year = {{2004}},
}