WIAS Preprint No. 1622, (2011)

An optimization method in inverse elastic scattering for one-dimensional grating profiles


  • Elschner, Johannes
  • Hu, Guanghui

2010 Mathematics Subject Classification

  • 35R30 74B05 78A46 35Q93


  • Diffraction grating, elastic waves, profile reconstruction, Tikhonov regularization, optimization method




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 Problems (2003) 19, 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 ($C^2$) 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.

Appeared in

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

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