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Homogenization of the Maxwell equations at fixed frequency

Publiceringsår: 2002
Språk: Engelska
Sidor: 38
Publikation/Tidskrift/Serie: Technical Report LUTEDX/(TEAT-7103)/1-38/(2002)
Dokumenttyp: Rapport
Ytterligare information: Published version: SIAM J. Appl. Math., 64(1), 170-195, 2003, doi:10.1137/S0036139902403366


The homogenization of the Maxwell equations at fixed frequency is addressed
in this paper. The bulk (homogenized) electric and magnetic properties of
a material with a periodic microstructure are found from the solution of a
local problem on the unit cell by suitable averages. The material can be
anisotropic, and satisfies a coercivity condition. The exciting field is generated
by an incident field from sources outside the material under investigation. A
suitable sesquilinear form is defined for the interior problem, and the exterior
Calder´on operator is used to solve the exterior radiating fields. The concept
of two-scale convergence is employed to solve the homogenization problem. A
new a priori estimate is proved as well as a new result on the correctors.



  • Electrical Engineering, Electronic Engineering, Information Engineering


  • Electromagnetic theory

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