Larisa Beilina (Department of Mathematical Sciences, Chalmers University of Technology and Gothenburg University, Sweden). Non-local imaging methods for solution of electromagnetic inverse problems.

In this talk I will briefly present survey of results on the solution of hyperbolic coefficient inverse problems (CIPs) using non-local optimization approach. This approach is based on the two-stage numerical procedure for the solution of CIPs. On the first stage an approximate globally convergent algorithm rigorously guarantee obtaining at least one point in a small neighborhood of the exact solution without any advanced knowledge of that neighborhood. On the second stage an adaptive finite element method refines the solution obtained on the first stage. An adaptive finite element method is based on a posteriori analysis which enables one to find spots where the maximum error of the solution is, and then to refine the spatial mesh locally with the feedback from the a posteriori error estimator. I will present numerical results of determination of the dielectric permittivity function in the time-dependent Maxwell's system for the electric field using only time-domain observations of the electric field at the backscattered side of the domain. These results show that the adaptivity leads to a dramatic enhancement of the reconstructed dielectric permittivity function.