Abstract

In this talk, we present stability estimates with explicit dependence of the wavenumber for scattering by both deterministic and random periodic structures for the Helmholtz equation. Moreover, an efficient numerical method based upon recursive linearization with mutlifreqencies for the corresponding inverse problem is discussed, i.e., recovering some key statistical properties of the profile for the unknown random periodic structure from boundary measurements of the scattered fields away from the structure. Numerical results are presented to demonstrate the reliability and efficiency of the proposed method.