Scattering from elongated objects: Direct solution in O(N log² N) operations

A recursive algorithm is presented for analysing TM and TE plane-wave scattering from two-dimensional elongated objects. The computational complexity and the memory requirements of the algorithm are O(N log² N) and O(N log N), respectively. The algorithm is based on the concept of a reduced representation and fast computation of fields that are radiated by quasialigned sources. While many existing fast algorithms for analysing electromagnetic scattering problems rely on iterative strategies, the proposed algorithm provides a direct solution to the scattering problem. The algorithm has a variety of potential applications, including the analysis of scattering from truncated and quasiperiodic structures, winglike structures, phased-array antennas and rough surfaces.