Convergence Rates of a Regularized Newton Method in Sound-Hard Inverse Scattering

Abstract

The iteratively regularized Gauss--Newton method is used to solve an inverse acoustic scattering problem with Neumann boundary conditions in two space dimensions, which is known to be nonlinear and severely ill posed. Some recent results on the speed of convergence for such problems are considered, and numerical experiments yield logarithmic convergence rates, as expected. Moreover, we present an efficient method to numerically evaluate the Frechet derivative using its characterization as a boundary value problem and prove fast convergence of this method.