Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm

Abstract

In this paper, we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditions by near-field measurements of acoustic waves. The algorithm relies on the Fréchet differentiability analysis of the locally rough surface scattering problem, which is established by reducing the original model into an equivalent boundary value problem with compactly supported boundary data. With a slight modification, the algorithm can be also extended to reconstruct the local perturbation of a non-local rough surface. Finally, numerical results are presented to illustrate the effectiveness of the inversion algorithm with the multi-frequency data.