Soboleva O.N.   Kurochkina E.P.  

The subgrid modeling for Maxwell's equations with multiscale isotropic random conductivity and permittivity

Reporter: Soboleva O.N.

Wave propagation in complex inhomogeneous media is an urgent problem in many fields of research. . In
order to compute the electromagnetic fields in an arbitrary medium, one must numerically solve Maxwell's equations. The large scale variations of coefficients as compared with wavelength are taken into account in these models with the help of some boundary conditions. The numerical solution of the problem with variations of parameters on all the scales require high computational costs. The spatial distributions of small-scale heterogeneities are not exactly known. It is customary to assume these parameters are random fields characterized by the joint probability distribution functions. The small-scale heterogeneities are taken into account by the effective parameters, coarsor grid methods, subgrid modeling. Simple equations are found on scales that can be numerically resolved. The solution to these equations must be closed to the averaged solution of the initial problem. In this paper 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 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 theoretical results obtained in the paper are compared with the results from direct 3D numerical simulation.