NUMERICAL GREEN’S FUNCTION SOLUTION OF THE HELMHOLTZ EQUATION

A promising new fast (of order N log₂N)method for finding the numerical solution of broad classes of partial differential equations is introduced. This method is referred to as the Iterative Dual Domain Method (IDDM), since its iterations occur in both transformed and untransformed domains. The specific example used is the Helmholtz equation for both homogeneous and almost arbitrarily inhomogeneous media. Preliminary indications of the algorithm’s performance are illustrated by examples of: wave focusing through a thick lens, scattering from an inclusion, and guided waves in layered media.