| 1. |
- Engström, Christian, et al.
(författare)
-
A comparison of two numerical methods for homogenization of Maxwell's equations
- 2004
-
Rapport (övrigt vetenskapligt)abstract
- When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coeffi- cients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.
|
|
| 2. |
|
|
| 3. |
|
|
| 4. |
- Engström, Christian, et al.
(författare)
-
Numerical methods for homogenization of Maxwell's equations
- 2004
-
Ingår i: URSI 2004 International Symposium on Electromagnetic Theory. - Pisa Univ. - 88-8492-252-6 ; s. 987-989
-
Konferensbidrag (refereegranskat)abstract
- When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. Two numerical methods for the determination of the homogenized coefficients are compared. Numerical examples, where extreme properties of the effective material are achieved in the two dimensional case, are presented
|
|
| 5. |
- Engström, Christian, et al.
(författare)
-
On two numerical methods for homogenization of Maxwell's equations
- 2007
-
Ingår i: Journal of Electromagnetic Waves and Applications. - VSP BV. - 0920-5071. ; 21:13, s. 1845-1856
-
Tidskriftsartikel (refereegranskat)abstract
- When the wavelength is much larger than the typical scale of the microstructure in a material, it is possible to define effective or homogenized material coefficients. The classical way of determination of the homogenized coefficients consists of solving an elliptic problem in a unit cell. This method and the Floquet-Bloch method, where an eigenvalue problem is solved, are numerically compared with respect to accuracy and contrast sensitivity. Moreover, we provide numerical bounds on the effective permittivity. The Floquet-Bloch method is shown to be a good alternative to the classical homogenization method, when the contrast is modest.
|
|
| 6. |
- Sjöberg, Daniel, et al.
(författare)
-
A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization
- 2003
-
Rapport (övrigt vetenskapligt)abstract
- Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.
|
|
| 7. |
- Sjöberg, Daniel, et al.
(författare)
-
A Floquet-Bloch Decomposition of Maxwell's Equations Applied to Homogenization
- 2005
-
Ingår i: Multiscale Modeling & Simulation. - Society for Industrial and Applied Mathematics. - 1540-3459. ; 4:1, s. 149-171
-
Tidskriftsartikel (refereegranskat)abstract
- Using Bloch waves to represent the full solution of Maxwell's equations in periodic media, we study the limit where the material's period becomes much smaller than the wavelength. It is seen that for steady state fields, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the nonvanishing Bloch waves, providing a new means of homogenization. The representation is valid for an arbitrary wave vector in the first Brillouin zone.
|
|
| 8. |
|
|
| 9. |
|
|
