Ukrainian Mathematical Bulletin

Volume 2, Issue 1, 2005 pp. 113-145.

Homogenization of Maxwell's Equations in Domains with Dense Perfectly Conducting Grids

Authors: Evgenii Ya. Khruslov
Author institution: Evgenii Ya. Khruslov, B. Verkin Institute for Low Temperature Physics and Engineering, NAS of Ukraine, Lenin Ave. 47, 61103, Kharkov, Ukraine

Summary: We consider Maxwell's equations in domains that are complements to connected, grid-like sets formed by intersecting thin wires. We impose the boundary conditions that correspond to perfectly conducting wires, and study the asymptotic behavior of solutions as grids are becoming thinner and denser. We derive a homogenized system of equations describing the leading term of the asymptotics. Assuming that a Korn-type inequality holds, we validate the homogenization procedure.

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