@Article{CiCP-24-435,
author = {Mingming Zhang and Junliang Lv},
title = {Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {2},
pages = {435--453},
abstract = {<p style="text-align: justify;">We are concerned with the profile reconstruction of a penetrable grating
from scattered waves measured above the periodic structure. The inverse problem is
reformulated as an optimization problem, which consists of two parts: a linear severely
ill-posed problem and a nonlinear well-posed problem. A Tikhonov regularization
method and a Landweber iteration strategy are applied to the objective function to
deal with the ill-posedness and nonlinearity. We propose a self-consistent method to
recover a potential function and an approximation of grating function in each iterative
step. Some details for numerical implementation are carefully discussed to reduce the
computational efforts. Numerical examples for exact and noisy data are included to
illustrate the effectiveness and the competitive behavior of the proposed method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0169},
url = {http://global-sci.org/intro/article_detail/cicp/12247.html}
}