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1 results

  • An Optimization Method in Inverse Elastic Scattering for One-Dimensional Grating Profiles

  • Johannes Elschner, Guanghui Hu
  • Journal:
    Communications in Computational Physics / Volume 12 / Issue 5 / November 2012
    Published online by Cambridge University Press:
    20 August 2015, pp. 1434-1460
    Print publication:
    November 2012

  • 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.