In this talk, we will introduce our recent advances in the multiscale analysis and algorithms for the electromagnetic properties of heterogeneous materials. First, we will briefly talk about the fundamental physical questions and the mathematical models from the classical electrodynamics to the semi-quantum models, then to the quantum electrodynamics (QED) and the quantum chromodynamics (QCD). Meanwhile, we will recall some known results about the multiscale analysis and algorithms for the classical Maxwell's equations and for the semi-quantum models. Second, we will focus on discussing the multiscale analysis and computation for Schrödinger-Poisson system in the effective mass approximation (EMA). Third, the multiscale method for Maxwell-Dirac system with rapidly oscillating discontinuous coefficients in novel materials will be reported. Finally, we will briefly introduce our recent results in the multiscale algorithm for simulating nonlocal optical response of metallic nanostructure arrays.

This talk is based on the joint work with Dr. Lei Zhang, Dr. Chupeng Ma, Dr. Yongwei Zhang and Prof. Yanping Lin.