Multiscale Numerical Algorithm for 3-d Maxwell’s Equations with Memory Effects in Composite Materials

This paper discusses the multiscale method for the time-dependent Maxwell’s equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integrodifferential equations to the stationary Maxwell’s equations by using the Laplace transform, to employ the multiscale asymptotic method to solve the stationary Maxwell’s equations, and then to obtain the computational solution of the original problem by employing a quadrature formula for computing the inverse Laplace transform. Numerical simulations are then carried out to validate the multiscale numerical algorithm in the present paper.