Summer School 2021 »Wave Phenomena: Analysis and Numerics«
- May 3rd, 2021 We are happy to announce that we will organize a summer school again. We are hoping and planning that it will be onsite. But we may change to a hybrid or even online only event.
This summer school is directed to PostDocs, PhD and advanced master students with a solid background in analysis and/or numerics of partial differential equations.
- Assoc. Prof. Lukas Einkemmer (University of Innsbruck, Austria) • Low-rank approximation for nonlinear kinetic problems
Due to the curse of dimensionality, solving high-dimensional partial differential equations numerically is extremely challenging. Complexity reduction techniques can alleviate the corresponding computational cost, but most classic methods assume a sufficiently regular solution. For hyperbolic equations this is often not a valid assumption. A promising approach to address such problems are so-called dynamical low-rank approximations. In this summer school we will provide an introduction to and discuss recent advances in constructing, analyzing, and implementing dynamical low-rank algorithms. In particular, we focus on applications to kinetic equations, which are widely used in plasma physics (e.g. in the study of Alfven waves).
- Dr. Anna Geyer (TU Delft, Netherlands) • Stability of nonlinear waves
Determining the stability of solutions is of central importance when analyzing partial differential equations arising in applications, as it is typically the stable solutions that are observed in practise. This analysis is particularly challenging when the models are nonlinear, and often relies on the presence of symmetries and corresponding conservation laws, which are a common phenomenon in physical models. In this course we give an introduction to stability theory for nonlinear Hamiltonian equations. We will draw inspiration from linearisation and energy methods for stability theory in finite-dimensional dynamical systems (ODEs) and show how these concepts can be adapted to the infinite-dimensional setting (PDEs). We will apply the theory to several equations modeling wave propagation.
From September 27-30, 2021, both speakers will give a lecture series accompanied by mini projects (with different focuses) for working in small groups. Additionally, there will be a poster session for PhD students and postdocs.
There is no fee. Please apply early, due to limited number of participants, until June 30th, 2021, by completing this email form and sending it to us. (Do you have trouble opening the link? Then copy & paste the email body manually and send it completed to admin∂waves.kit.edu.) Female PhD and Master's students are particularly encouraged to attend.
Notice: Please apply early for a visa (if you need one) to enter Germany.
Laurette Lauffer and Christian Knieling via E-Mail: admin∂waves.kit.edu