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

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 East 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(N-4/3) 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.