Fast inhomogeneous plane wave algorithm for the fast analysis of two‐dimensional scattering problems

Abstract

A novel algorithm, the fast inhomogeneous plane wave algorithm (FIPWA), has been developed to accelerate the solution of integral equations pertinent to the analysis of the scattering from two‐dimensional perfect electric conducting surfaces. Unlike the fast steepest descent path algorithm, the proposed technique directly interpolates the far‐field pattern of the source group and matches it along a modified steepest descent path. A novel approach, which results in a diagonal translator with built‐in interpolation coefficients, is proposed. The computational complexity per matrix‐vector multiplication of a two‐level implementation of the proposed FIPWA is O(N4/3) and the multilevel implementation further reduces the complexity to O(NlogN), where N is the number of unknowns in the discretized integral equation. It is shown that this technique outperforms the previously developed fast methods such as the fast mulitpole method and the ray‐propagation fast multipole algorithm.