141. |
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144. |
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146. |
- Sjöberg, Daniel
(author)
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Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition
- 2005
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In: Multiscale Modeling & Simulation. - : Society for Industrial & Applied Mathematics (SIAM). - 1540-3459 .- 1540-3467. ; 4:3, s. 760-789
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Journal article (peer-reviewed)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.
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147. |
- Sjöberg, Daniel
(author)
-
Homogenization of dispersive material parameters for Maxwell's equations using a singular value decomposition
- 2004
-
Reports (other academic/artistic)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 infinitely large compared to the unit cell.
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