1. Roland Potthast. Group leader. Dr. Potthast has worked on scientific and industrial projects for more than 15 years, leading a range of new developments in the mathematical theory and applications of inverse modelling / inverse problems. He is a well-known author in the area, with book contributions and a range of well-cited publications on new methods, analysis and applications. Dr. Potthast serves on the steering committee of several international conferences on inverse problems and for the inverse problems international association (IPIA).
2. Martin Wannert. In a collaboration with the Research Center Jülich Martin Wannert works on mathematical algorithms for Magnetic Tomography. He has developed several projection algorithms which incorporate different type of a-priori knowledge into the inversion schemes. Currently, he is working on a new uniqueness proof for current reconstructions from fuel cells. In general, the current reconstruction is highly non-unique (see Hauer, Kühn, Potthast 2005), however, for the special case of a fuel cell uniqueness can be shown. Further, Martin Wannert works on the evaluation of the maximal potential of magnetic tomography and on the application of the algorithms to real data by managing a measurement device jointly developed by TomoScience, Wolfsburg, the research center Jülich and our research group in Reading and Göttingen. One publication is submitted, a second publication is in preparation.
3. Muhammad Zaighum-Zia. Muhammad Zaighum-Zia works on inverse problems in fluid dynamics. As a starting point he is formulating the point source method for flow field reconstructions for the Stokes and the Oseen equation and implemented the forward and inverse problems. A publication is in preparation. Further steps will be carried out by investigating the applicability of sampling and probe methods for these equations, in particular looking at the singular-sources method (Potthast 1998) and the no-response test (Luke-Potthast 2003).
4. Corinna Burkard. On a project about Optical Security Devices Corinna Burkard investigates direct and inverse scattering in three dimensions. In a first step she has solved the inverse acoustic scattering problem by a rough surface in three dimensions using the Kirsch-Kress method, i.e. the adaption of the fields by a potential approach and the search for an unknown surface by a minimization technique. She develped the convergence analysis for this situation, which involves a number of sincere difficulties due to the unbounded geometry of the domain under consideration. Further, she has implemented the method and showed the numerical feasibility of the method. A first publication is in preparation. In a second step she now looks at the electromagnetic problem in three dimensions, where the design of new optical security devices by simulation of scattering processes is the target of this ambitious project in collaboration with Prof. Geoff Michell, Center for Advanced Microscopy, Prof. Chandler-Wilde, Mathematics and Dr David Ezra, Oxford.
5. Boris Marx. As a diplom student Boris Marx has worked on the optimal choice of measurement points for Magnetic Tomography. He has formulated a hybrid evolutionary gradient method for the solution of this "meta"-inverse problem. The method consists of a two-population evolutionary algorithm where the mutations of the second population are deterministic and are carried out by several steps of a gradient method. This hybrid scheme combines the strength of both algorithms and avoids their disadvantages. Currently, Boris Marx is now a PhD student in the Graduiertenkolleg in Göttingen jointly supervised by Kress and Potthast. He continues work on magnetic tomography investigating stochastic algorithms and data assimilation techniques for time-dependent reconstruction problems.
6. Ndifreke Etik. Electrical Resistance Tomography (ERT) is a basic and important technology employed for geophysics and archeology. Ndi is working on the optimization of measurement points for electrical resistance tomography in archeaological applications. The project is jointly supervised with Dr. Timothy Astin from the department of Archeaology at the Unviersity of Reading.
7. Natalie Lowery Jointly supervised with Dr Maria Vahdati from Engineering the project investigates the use of discrimination algorithms in connection with inversion as it is used for example in static or dynamic magnetic tomography. The interplay of methods which are popular in artificial intelligence and the broad collection of tools which has been developed in the field of tomography and inverse problems is one of the basic research challenges for applied inverse problems.
8. Alexander Moodey. Data assimilation techniques are widely used in weather forecasting and hydrology. The basic task is to determine the current state of a complex system by combining measurements and model calculations using the past state of the system. The dynamical systems under consideration are usually highly complex and nonlinear and one needs to employ a huge number of unknown system parameters. It is well-known that these problems are ill-conditioned, i.e. data error can be strongly amplified. Thus, proper stabilization methods need to be employed for the stable determination of system states and are integrated into assimilation schemes. Various variational and stochastic assimilation algorithms have been developed, e.g. 3DVar, 4DVar and the ensemble Kalman Filter. The task of the project is the investigation of the instability and the stabilization properties of current assimilation algorithms with tools from regularization theory and the theory of ill-posed problems. In particular, we will study assimilation for a hierarchy of typical nonlinear systems ranging from very simple to complex systems with the task to derive general results on the stabilization behaviour of the algorithms under particular error types which naturally occur within important applications. This project is jointly supervised with Prof. Peter Jan van Leeuven from Meteorology and Dr Amos Lawless from Math at Reading.

9. Tobias Schwab. As assistant Tobias is working on scientific and industrial projects as well as the public engagement projects of the group, in particular on the open scientist initiative.
10. Daniel Langhans. Daniel is software programmer. He is supporting the work of the group on the programming side, both for scientific, industrial and public engagement projects.
11. Florian Lackert. System Administrator. Florian is working on the administration of various computer systems which are used by the group.

Previous Research Students and Postdocs

1. Eric Heinemeyer (PhD 2004-2007, PostDoc 2007-8), Graduate School
2. Fabrice Delbary (PostDoc 2006), BMBF
3. Jochen Schulz (PhD 2001-2007)
4. Fahmi ben Hassen (PostDoc 2004-2005), NFG
5. Klaus Erhard (PhD 2002-2005), NFG
6. Russell Luke (PostDoc 2001-2003), NFG
7. Lars Kühn (PhD 2001-2005), NFG
8. Kuo-Ming Lee (PhD 2003, Kress first supervisor), NFG

NFG = Nachwuchs-Forscher Gruppe (Young Researchers Group)