TY - JOUR
T1 - Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data
AU - Mingming Zhang & Junliang Lv
JO - Communications in Computational Physics
VL - 2
SP - 435
EP - 453
PY - 2018
DA - 2018/08
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0169
UR - https://global-sci.org/intro/article_detail/cicp/12247.html
KW - Profile reconstruction, optimization method, Tikhonov regularization, periodic transmission problem.
AB - <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>