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–Müller radiation condition is utilized to truncate infinite domain problems. Numerical experiments are then carried out to validate the theoretical results.