# A Generalized Recursive Algorithm for Wave-Scattering Solutions in Two Dimensions

## Abstract

A generalized recursive algorithm valid for both the E<inf>z</inf>and H<inf>z</inf>wave scattering of densely packed scatterers in two dimensions is derived. This is unlike previously derived recursive algorithms which have been found to be valid only for E<inf>z</inf>polarized waves [l]-[7]. In this generalized recursive algorithm, a scatterer is first divided into N subscatterers. The n-subscatterer solution is then used to solve the (n + n')-subscatterer solution. The computational complexity of such an algorithm is found to be of O(N<sup>2</sup>) in two dimensions, and mean-while, providing a solution valid for all angles of incidence. This is better than the method of moments with Gaussian elimination which has an O(N<sup>3</sup>) complexity. © 1992 IEEE