DFG Project: "Direct and inverse scattering problems for elastic waves"


July 16, 2009 - July 15, 2012


Project Head: J. Elschner (Nonlinear Optimization and Inverse Problems)
Project Researcher: G. Hu (Nonlinear Optimization and Inverse Problems)

Project Description:

Direct and inverse scattering problems for elastic waves occur in many applications in natural sciences and engineering. The project is devoted to the investigation of scattering of time harmonic elastic waves by (in general) unbounded surfaces and interfaces in the case of periodic structures (diffraction gratings) as well as in the non-periodic case (rough surfaces). This leads to direct and inverse boundary value problems for the Navier equation in unbounded domains, the analytical and numerical treatment of which is challenging. One objective of the project is to develop a new solvability theory (existence and uniqueness of solutions, Fredholm property) for the direct scattering problems based on variational formulations. In this respect diffractive structures with non-smooth interfaces and several elastic materials are of particular interest. A second aim of the project is concerned with uniqueness results and reconstruction methods for the inverse problem of determining the scattering object by near and far field measurements of the scattered elastic field. For both tasks, inspiration should be taken from recent results in the case of acoustic and electromagnetic waves.