Applied Mathematics Seminar: Lukas Einkemmer
Topic
Higher-order structure preserving low-rank methods for kinetic problems
Speakers
Details
Low-rank methods have proven their utility as a complexity reduction technique for kinetic equations, both in the collisionless and collisional regimes (see, e.g., the recent review article https://doi.org/10.1016/j.jcp.2025.114191). Since the resulting low-rank factors are lower-dimensional, such methods can overcome the famous curse of dimensionality. This is usually the most severe constraint for performing kinetic simulations in practice. In their classic form, these methods, however, do not conserve any of the invariants or underlying conservation laws. In this talk, we will present our recent work on developing structure-preserving dynamical low-rank methods of arbitrary order.
Additional Information
This is a hybrid event. A Zoom link will be provided soon.
Speaker Bio:
Lukas Einkemmer is a full professor at the University of Innsbruck, from which he also obtained his PhD in 2014. His research focuses on the development and analysis of efficient algorithms for solving partial differential equations using modern high-performance computer systems, in particular high-dimensional problems such as those used in plasma physics. He has authored some of the pioneering work on using dynamical low-rank approximation for kinetic problems and formulating such methods in a continuous setting. He has also made significant contributions to structure-preserving algorithms both for classic and low-rank methods. This includes work on the construction, analysis, and efficient implementation of splitting methods, exponential integrators, semi-Lagrangian methods, and discontinuous Galerkin schemes, among others. For his research, he has been awarded the SciCADE New Talent award in 2015 and later the prize of the state capital Innsbruck for scientific research.
