A multiscale approach and a hybrid FE-BE algorithm for heterogeneous scattering of Maxwell's equations

In this paper we discuss the multiscale approach for the scattering problem of Maxwell's equations in a heterogeneous material with a periodic microstructure. The new contributions in this paper are the determination of the multiscale correctors and the strong convergence in the norm of the space H(curl;Ω) with an explicit rate for the approximate solutions (see Theorem 2.4). Consequently, we present a multiscale hybrid finite element method-boundary element method (FE-BE). The numerical examples are carried out to validate the theoretical results of this paper.