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Volume 12, Issue 5
An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles

Johannes Elschner & Guanghui Hu

DOI: 10.4208/cicp.220611.130112a

Commun. Comput. Phys., 12 (2012), pp. 1434-1460.

Published online: 2012-12

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  • Abstract

Consider the inverse diffraction problem to determine a two-dimensional periodic structure from scattered elastic waves measured above the structure. We formulate the inverse problem as a least squares optimization problem, following the two-step algorithm by G. Bruckner and J. Elschner [Inverse Probl., 19 (2003), 315–329] for electromagnetic diffraction gratings. Such a method is based on the Kirsch-Kress optimization scheme and consists of two parts: a linear severely ill-posed problem and a nonlinear well-posed one. We apply this method to both smooth (C2) and piecewise linear gratings for the Dirichlet boundary value problem of the Navier equation. Numerical reconstructions from exact and noisy data illustrate the feasibility of the method. 

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@Article{CiCP-12-1434, author = {Johannes Elschner and Guanghui Hu}, title = {An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {1434--1460}, abstract = {

Consider the inverse diffraction problem to determine a two-dimensional periodic structure from scattered elastic waves measured above the structure. We formulate the inverse problem as a least squares optimization problem, following the two-step algorithm by G. Bruckner and J. Elschner [Inverse Probl., 19 (2003), 315–329] for electromagnetic diffraction gratings. Such a method is based on the Kirsch-Kress optimization scheme and consists of two parts: a linear severely ill-posed problem and a nonlinear well-posed one. We apply this method to both smooth (C2) and piecewise linear gratings for the Dirichlet boundary value problem of the Navier equation. Numerical reconstructions from exact and noisy data illustrate the feasibility of the method. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.220611.130112a}, url = {http://global-sci.org/intro/article_detail/cicp/7341.html} }
TY - JOUR T1 - An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles AU - Johannes Elschner & Guanghui Hu JO - Communications in Computational Physics VL - 5 SP - 1434 EP - 1460 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.220611.130112a UR - https://global-sci.org/intro/article_detail/cicp/7341.html KW - AB -

Consider the inverse diffraction problem to determine a two-dimensional periodic structure from scattered elastic waves measured above the structure. We formulate the inverse problem as a least squares optimization problem, following the two-step algorithm by G. Bruckner and J. Elschner [Inverse Probl., 19 (2003), 315–329] for electromagnetic diffraction gratings. Such a method is based on the Kirsch-Kress optimization scheme and consists of two parts: a linear severely ill-posed problem and a nonlinear well-posed one. We apply this method to both smooth (C2) and piecewise linear gratings for the Dirichlet boundary value problem of the Navier equation. Numerical reconstructions from exact and noisy data illustrate the feasibility of the method. 

Johannes Elschner and Guanghui Hu. (2012). An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles. Communications in Computational Physics. 12 (5). 1434-1460. doi:10.4208/cicp.220611.130112a
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