Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition
Författare
Summary, in English
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.
Publiceringsår
2005
Språk
Engelska
Sidor
760-789
Publikation/Tidskrift/Serie
Multiscale Modeling & Simulation
Volym
4
Issue
3
Dokumenttyp
Artikel i tidskrift
Förlag
Society for Industrial and Applied Mathematics
Ämne
- Electrical Engineering, Electronic Engineering, Information Engineering
Nyckelord
- Maxwell's equations
- singular value decomposition
- homogenization
- Bloch waves
- dispersive media
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1540-3459