Accurate analysis of large-scale periodic structures using an efficient sub-entire-domain basis function method

An efficient sub-entire-domain (SED) basis function method has been proposed to analyze large-scale periodic structures with finite sizes accurately. The SED basis function is defined on the support of each single cell of the periodic structure. After introducing dummy cells with respect to an observation cell, the real physics of SED basis function is captured accurately by solving a small-size problem. Further analysis has shown that all kinds of SED basis functions used in the periodic structure can be obtained by solving a single small problem. Hence, the original large-scale problem involving N=N₀M unknowns is decomposed into two small-size problems, one of which contains 9M unknowns and the other of which contains only N₀ unknowns. Here, N₀ is the total cell number in the periodic structure and M is the number of subdomain basis functions in each unit cell. Several examples are given to test the validity and efficiency of the proposed method. Numerical results from the new method have excellent agreements with those from the conventional method of moments. However, the CPU time has been greatly reduced.