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Volume 24, Issue 2
Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data

Mingming Zhang & Junliang Lv

DOI: 10.4208/cicp.OA-2017-0169

Commun. Comput. Phys., 24 (2018), pp. 435-453.

Published online: 2018-08

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  • Abstract

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.

  • Keywords

Profile reconstruction, optimization method, Tikhonov regularization, periodic transmission problem.

  • AMS Subject Headings

35R30, 78A46, 78M50

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0169}, url = {http://global-sci.org/intro/article_detail/cicp/12247.html} }
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 -

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.

Mingming Zhang and Junliang Lv. (2018). Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data. Communications in Computational Physics. 24 (2). 435-453. doi:10.4208/cicp.OA-2017-0169
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