The project investigates the reconstruction of a perfectly conducting obstacle within a heterogeneous conductive medium from electrostatic measurements. This setup is intended to represent realistic side constraints for, say, the detection of buried land mines in a (heterogeneous) ground.
The macroscopic specification of this problem corresponds to an elliptic differential equation, which requires a very fine discretization to resolve the heterogeneous structure of the medium. This way, the problem leads to an extremely large linear system, whose solution would be prohibitively expensive. The project aims to exploit a different approach based on Monte-Carlo and multi body simulations that simulate the physical processes on a microscopic scale. Note that the heterogeneity of the medium, that is to be averaged on the microscopic scale, must be a "small" perturbation of a homogeneous reference to prevent anomalous transport or so-called Anderson localization.
The intension of the project are new findings, whether methods, that have previously been developed in Mainz to solve the inverse problem within a homogeneous background, are also applicable or can be extended to heterogeneous media.