Biography

Research Interests
I have beed dedicated to moving the frontiers of computation-based neuroscience towards a research field that is driven by physical first principles, numerical methods and large scale simulations.Computational methods in neuroscience are currently based on analogies, rather than detailed physical models. Typically the geometry of single cells and networks is neglected, resulting in compartment models, which are not adequate for describing the relevant details in signal processing.
My group therefore has focussed strongly on modeling and simulating biological processes, e.g. in brain cells, by means of continuum theory and the inclusion of detailed morphologies, and on showing at such models are feasible in the context of complex biology. In the last years we have pioneered detailed computational modeling and simulation for investigating the structure-function interplay in biological systems. We were able to show that cells and organelles alter their morphology in order to
adapt their computational properties for long term information storage.
In order to include detailed morphologies into numerical simulations, we developed, to my knowledge, the first fully automated reconstruction algorithm, that operates on microscopy data to generate surface and volume grids. Additionally, we have developed AnaMorph, a parametric reconstruction method based on theory from discrete geometry, that generates three-dimensional computational domains from low-dimensional information. To then model and simulate nonlinear physical behavior on realistic, hence complex, computational domains, numerical methods were
further developed and optimized towards complex-domain problems by my research group. Research in numerics and computational mathematics has been dedicated to developing a novel subdivision volume geometric multigrid method, that automatically generates multigrid hierarchies with high element quality, such that matrix condition numbers and other numerically relevant parameters are optimized. This has allowed us to simulate real-life problems where classical strategies fail.
With increasing level of modeling detail, problem size and computational complexity increases as well. While my group’s aim is to simulate processes in full three-dimensional detail wherever it becomes necessary, we have also developed hybrid-dimensional approaches to couple regions of high dimensional representation with low-dimensional approximations. By developing special transfer operators this allows us to compute large-scale problems with local high-dimensional representation.
This hybrid-dimensional idea has similarities to adaptive grid refinement that is based on error estimates. To further optimize mathematical methods for large-scale applications, we developed an a posteriori, residuum-based, finite volume error estimator for coupled diffusion-reaction problems with nonlinear interface conditions.