When incorporating the detailed geometry in numerical simulations one can investigate the structure-function relations in great detail. This is necessary for developing individualized strategies in medical and biological research. On one hand, the complexity of the resulting computational domain influences the numerical solution – here grid regularity plays a role – on the other hand the degrees of freedom in the grid become very large. To deal with such high-dimensional problems requires us to improve mathematical methods for a new set of applications. Scaling properties of such methods for massively parallel computing is not only essential for the solvers, but also for the handling of very large computational grids.
Scalable Algorithms for High-Performance Computing
Computing the electrical activity of very large neuronal networks is computationally challenging, especially when the morphology of single neurons are resolved at a high level of detail. We are developing numerical methods to solve network sizes above 10,000 neurons on massively parallel computing architectures. Network anatomy can be generated with NeuGen to run simulations on an entire cortical column where each of the 10,000s of neurons is represented by an average of 300 degrees of freedom.
(Simulation by M. Breit & L. Reinhard)
Solving problems on realistic three-dimensional geometries allows us to study how geometry, a time-dependent parameter in biology, influences cellular function. Ultra-structural computing, where the dynamics of ions are governed by diffusive and electrical fluxes governed by the detailed sub-cellular architecture requires sub-nanometer resolution at membranes. Scalable, adaptive and higher order methods for solving such problems are a core aspect of our work.
(Image by M. Breit)
GPU-based image reconstruction allows us to automatically generate surface and volume discretizations of cells and organelles from raw microscopy data. These reconstructions can be used within detailed numerical simulations on high-performance computers.
(Image by G. Queisser)