B. Hu et al., Fast inhomogeneous plane wave algorithm for the fast analysis of two-dimensional scattering problems, RADIO SCI, 34(4), 1999, pp. 759-772
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 con
ducting surfaces. Unlike the East steepest descent path algorithm, the prop
osed technique directly interpolates the far-field pattern of the source gr
oup and matches it along a modified steepest descent path. A novel approach
, which results in a diagonal translator with built-in interpolation coeffi
cients, is proposed. The computational complexity per matrix-vector multipl
ication 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 meth
ods such as the fast mulitpole method and the ray-propagation fast multipol
e algorithm.