Upscaling for the time-harmonic Maxwell equations with heterogeneous magnetic materials
Jens Eberhard · Physical Review E · 2005
This paper presents a theoretical method for the upscaling of the time-harmonic Maxwell equations. We use the eddy current approximation of the Maxwell equations to describe the fields in heterogeneous materials. The magnetic permeability of the media is assumed to have random heterogeneities given by a Gaussian random field. The upscaling is based on the coarse graining method which applies projections and Green's function formalism in Fourier space to scale the electric field. An upscaled Maxwell equation is derived which includes an effective magnetic permeability tensor. The effective permeability explicitly depends on the given scale for the upscaling. The scale-dependent permeability is calculated by a second-order perturbative expansion, and we discuss the future verification and the application of the results.