Numerical Reconstruction of Locally Rough Surfaces with a Newton Iterative Algorithm (Communications in Computational Physics, 2023)
In this paper, we propose a Newton iterative algorithm to numerically reconstruct a locally rough surface with Dirichlet and impedance boundary conditionsby 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 problemwith compactly supported boundary data. With a slight modification, the algorithmcan 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 inversionalgorithm with the multi-frequency data.
Keywords: Newton iterative algorithm; Fréchet derivative; inverse scattering; locally rough surface; Dirichlet condition; impedance condition; multi-frequency data.