Multipole-free fast inhomogeneous plane wave algorithm

Solving radiation and scattering problems in the vicinity of a half-space or stratified medium with integral equation methods is complicated, and slowed by computation of expensive Sommerfeld integrals. In this paper, a new formulation of the spectral layered media Green's function is presented. It is demonstrated for a simple scattering problem in the new fast algorithm called the Multipole-Free Fast Inhomogeneous Plane Wave Algorithm (MF-FIPWA). MF-FIPWA is shown to scale as
$\mathcal{O}$
(N log N) in memory usage and processing time. Additional advantages include rigorous treatment of reflected contributions, simplicity in design, and mathematical insight into the fast algorithm.