报告人：Julian Koellermeier (Bernoulli Institute, University of Groningen, the Netherlands)
Abstract: The high dimension of many mathematical models in science and engineering leads to prohibitively large computational cost for even an approximate numerical solution. However, an accurate solution of the full model is often not even necessary, as only a small set of variables suffices to characterise the main behaviour of the solution. This poses the question of model reduction: How can we efficiently reduce the complexity of the model and arrive at a reduced model, that is both sufficiently accurate and computationally feasible?
In this talk, we fist briefly discuss different model reduction techniques for kinetic equations. We then focus on moment models as one way to reduce the full model to a set of analytical, lower-dimensional equations. The benefits of moment models are the mathematically sound derivation, their hierarchical structure, and the possibility to assess analytical properties of the model from the resulting equations.
We consider, among other, examples from rarefied gases and free-surface flows and illustrate those by numerical simulations.
Speaker: Dr. Julian Koellermeier is an Assistant Professor in the Computational Mathematics group of the Bernoulli Institute within the Faculty of Science and Engineering and associated with the Groningen Cognitive Systems and Materials Center (CogniGron). Previously, he was a Marie-Curie postdoc at KU Leuven, and held positions at Peking University, and Free University Berlin. He obtained his PhD in Applied Mathematics from RWTH Aachen University.
Julian's research is interdisciplinary and situated at the interface of applied mathematics, numerical simulation, and computational engineering. He develops mathematical models and numerical simulations, e.g., for applications in rarefied gases, nuclear fusion, and geophysical flows.