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