Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/221313
- author
- Sjöberg, Daniel LU
- organization
- publishing date
- 2005
- 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
- Society for Industrial and Applied Mathematics
- 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
- 2016-04-01 12:11:43
- date last changed
- 2022-01-27 00:16:14
@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}}, keywords = {{Maxwell's equations; singular value decomposition; homogenization; Bloch waves; dispersive media}}, language = {{eng}}, number = {{3}}, pages = {{760--789}}, publisher = {{Society for Industrial and Applied Mathematics}}, 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}}, doi = {{10.1137/040614153}}, volume = {{4}}, year = {{2005}}, }