A FAFFA-FIPWA algorithm for two-dimensional electromagnetic scattering problem

Recently, rapid progress is made in fast algorithm of integral equation(IE) method to accelerate matrix-vector multiplication which occurs in iterative method, thus making it possible to solve large scalar problem through numerical techniques. In this paper, A fast far-field approximation (FAFFA) [C.C. Lu et al, 1995] technique is combined into the fast inhomogeneous plane wave algorithm (FIPWA) [Bin Hu et al, 1999], namely FAFFA-FIPWA, to further speed up matrix-vector multiplication in the process of iteration. The interaction is divided into three regions: near region, resonant region and far region. In near region, the coupling is computed directly, and in resonant region, the FIPWA is needed. When in far region, the pure FIPWA is not necessary again since only one direction k₀ makes main contribution in translation from source point to field point in this case, so the FAFFA is used in this region.