The Subgrid Modeling for Maxwell's Equations With Multiscale Isotropic Random Conductivity and Permittivity

Abstract

Abstract-The effective coefficients for Maxwell's equations in the frequency domain are calculated for a multiscale isotropic medium by using a subgrid modeling approach. The correlated fields of conductivity and permeability are approximated by Kolmogorov's multiplicative continuous cascades with a lognormal probability distribution. The wavelength is assumed to be large as compared with the scale of heterogeneities of the medium. The permittivity ε(x) and the electric conductivity σ(x) satisfy the condition σ(x)/(ωε(x)) < 1, where ω is the cyclic frequency. The theoretical results obtained in the paper are compared with the results from direct 3D numerical simulation.