(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Elschner, Johannes; Hu, Guanghui
This paper is concerned with the direct and inverse scattering of time-harmonic plane elastic
waves by unbounded periodic structures (diffraction gratings). We present a variational approach
to the forward scattering problems with Lipschitz grating profiles and give a survey of recent
uniqueness and existence results. We also report on recent global uniqueness results within the
class of piecewise linear grating profiles for the corresponding inverse elastic scattering problems. Moreover, a discrete Galerkin method is presented to efficiently approximate solutions of direct
scattering problems via an integral equation approach. Finally, an optimization method for solving
the inverse problem of recovering a 2D periodic structure from scattered elastic waves measured
above the structure is discussed.
