An improved operator expansion algorithm for direct and inverse scattering computations

Abstract

In the first part of the paper we present an implementation of Milder's operator expansion formalism for acoustic scattering from a rough non-periodic surface. Our main contribution to the forward-field calculation is the development of two accurate ways of computing the order-zero normal differentiation operator N ₀. The accuracy of our implementation is tested numerically. In the second part of our paper we apply this approach, combined with a continuation method, to an inverse scattering problem. The resulting scheme performs significantly better than the classical first-order methods.