Multiscale analysis and algorithm of transient electromagnetic scattering from heterogeneous materials

The paper is concerned with the multiscale analysis of the scattering problem for three-dimensional time-dependent Maxwell's equations in heterogeneous materials. Firstly, an exact transparent boundary condition is developed to reduce the scattering problem into an initial-boundary value problem in heterogeneous materials. Secondly, the multiscale asymptotic expansions of the solution for the reduced problem and an explicit convergence rate for the approximate solutions are presented. Finally, a multiscale Crank-Nicolson mixed finite element method is proposed where the first order approximation of the Silver-Muller radiation condition is utilized to truncate infinite domain problems. Numerical experiments are then carried out to validate the theoretical results. (c) 2021 Elsevier B.V. All rights reserved.