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

Abstract

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.