Convergent Born series for large refractive indices

Abstract

It is shown that a generalized overrelaxation method, when applied to the domain integral equation that arises in scattering by penetrable objects, results in a convergent iterative solution. This modified Born series converges when the original Born series diverges for a wide range of indices of refraction and scatterer size. Moreover the modified series converges more rapidly than the original Born series in those cases for which the original series converges. Numerical examples demonstrating the effectiveness of this method are presented in one, two, and three dimensions.