Homogenization via Harmonic Analysis

Homogenization, which reduces the cost of numerical simulation in materials with repetitive structure, is a promising approach to the design of photonic crystals and metamaterials. But its mathematical foundations may seem daunting. A link with standard harmonic analysis is indicated here ("homogenization as approximate Fourier analysis for lattice group actions"), which should help clarify the issue. New applications, to high-frequency problems are suggested