| Abstract: |
| The numerical solution of kinetic equations often requires a high computational effort and memory cost due to the potentially six-dimensional phase space. One approach to overcome this difficulty is the reduced order method dynamical low-rank approximation. It has recently gained an increasing interest as it has been shown to provide accurate numerical solutions of kinetic PDEs in various applications while reducing the computational time significantly.
This talk will focus on a research project that has the goal to devise an efficient numerical method for solving a BGK-type kinetic equation
$$ \partial_t f+ v \cdot \nabla f= \sigma (M - f) . $$
Our approach has the potential to bring about large savings in computational time. We build on the low-rank approximation technique used by Einkemmer, Jingwei Hu, Ying, SIAM J. Sci. Comput. (2021). We show how we have made progress in reducing the numerical effort even further by proving stability estimates for a related system of kinetic equations, see Baumann, Einkemmer, Klingenberg, Kusch, SIAM J. Sci. Comput. (2024).
This is joint work with Lena Baumann (W\urzburg, Germany), Lukas Einkemmer (Innsbruck,Austria) and Jonas Kusch (As, Norway). |
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