A new formalism for time-dependent electromagnetic scattering from a bounded obstacle

Abstract

In this paper a time-dependent three-dimensional electromagnetic scattering problem is considered. Let R3 be the three-dimensional real Euclidean space filled with a medium of electric permittivity e, magnetic permeability μ and zero electric conductivity. The quantities e, μ are positive constants and there are no free charges in the space and the free current is taken to be zero. Let Ω⊂R3 be a bounded simply connected obstacle with a locally Lipschitz boundary ∂Ω, that is assumed to have a nonnegative constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. An incoming electromagnetic wave packet that hits Ω is considered, and a method that solves the Maxwell equations to compute the corresponding electromagnetic field scattered by Ω as a superposition of time harmonic electromagnetic waves is proposed. These time-harmonic electromagnetic waves are the solutions of exterior boundary-value problems for the vector Helmholtz equation with the divergence-free condition and they are computed with an `operator expansion' method that generalizes the method presented by L. Fatone et al.[J. Math. Phys. 40 (1999) 4859–4887]. The method proposed here is computationally very efficient. In fact, it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from a numerical and a physical point of view. The quantitative character of the numerical experiments shown is established. The website: http://www.econ.unian.it/recchioni/w4/ contains some animations relative to the numerical experiments.