The compact course Mathematical Complexity Reduction: Scientific Computing (LSF) will be held within summer term 2018 for PhD students of the Research Training Group. Interested master and PhD students, e.g., from the Faculty of Mathematics or the IMPRS, may also participate if places are available (Wahlfach).
The first two days of the course are dedicated to an introduction to the finite element method for discretizing partial differential equations and numerical techniques for the solution of the arising linear systems of equations. We focus on multigrid methods that allow optimal computational complexity. We will then focus on three rather novel techniques of Scientific Computing that directly address high-dimensional problems and their complexity reduction. The first is data-driven modeling, allowing the identification of low complexity models from experimental and simulation data. The second is model order reduction, which allows the fast simulation of dynamical and parametric models in a multi-query context, e.g., when parameters are varied. Finally, the last day will be devoted to tensor techniques for computational problems requiring (or employing) data structures with more than two dimensions.
In order to register, show up at 9am on the first day.