Inverse Problems in Electrostatics and Electrodynamics

• Antragsteller: Professor Dr. Martin Hanke-Bourgeois; Professor Dr. Andreas Kirsch
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2011 bis 2014
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 191118443

The purpose of this project is the study of inverse obstacle problems that arise (i) in time-harmonic electromagnetic scattering problems, and (ii) in impedance tomography (electrostatics). These are nonlinear and highly ill-posed problems, and basic questions are the identifiability of the penetrable or impenetrable obstacles or inhomogeneous media. We seek also for numerical algorithms to reconstruct these obstacles or media.In this project we will focus on analytical and numerical questions that arise in the context of so-called sampling methods (the factorization method being a very prominent example), but are not limited to these methods in their applicability. One of these questions concerns the existence and distribution of transmission eigenvalues, which correspond to frequencies that must be avoided when sampling methods are used for the reconstruction. Another line of research deals with heterogeneous media, and with the interconnection of the Dirichlet-Neumann operator and so-called local time-processes that arise in a probabilistic interpretation of the forward problem of impedance tomography.

• DFG-Verfahren: Sachbeihilfen
• Internationaler Bezug: China, Finnland
• Beteiligte Personen: Professor Dr. Jijun Liu; Professor Lassi Päivärinta