Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data

Numerical Method of Profile Reconstruction for a Periodic Transmission Problem from Single-Sided Data

Year:    2018

Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2017-0169

Communications in Computational Physics, Vol. 24 (2018), Iss. 2 : pp. 435–453

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Profile reconstruction optimization method Tikhonov regularization periodic transmission problem.