Fast algorithms for large-scale periodic structures

It is very important to study the electromagnetic properties of periodic structures due to their wide applications. We propose two fast algorithms to analyze periodic structures based on the CG-FFT method using sub-entire-domain (SED) basis functions. For a large-scale periodic structure consisting of N₀ = N_xN_y elements, the number of unknowns is only N₀ in use of SED basis functions, and we only need to evaluate O(N₀) matrix elements instead of N₀². Numerical results are given to test the accuracy and efficiency of the proposed algorithms.