This workshop is aimed at the participants in the Trimester Program "Computational multifidelity, multilevel, and multiscale methods". It is not possible to apply only for this workshop.
Organizers:
- Sara Avesani (Università della Svizzera Italiana)
- Carles Beall (Stevens Institute of Technology)
- Moritz Hauck (Karlsruhe Institute of Technology)
- Maher Khrais (University of Bonn)
- Dilini Kolombage (Institute for Numerical Simulation, University of Bonn)
- Roland Maier (Karlsruhe Institute of Technology)
- Florian Schneider (University of Leipzig)
- Lucia Swoboda (Chalmers University of Technology and University of Gothenburg)
- Johan Wärnegård (Chalmers University)
Description:
In many applications, classical discretization methods are limited when dealing with heterogeneous microstructures, especially when variations occur over multiple scales. Globally resolving such structures can lead to an intractable number of degrees of freedom, and not resolving them generally leads to incorrect approximations. Problem-adapted approximation spaces provide an elegant solution by effectively bridging scale differences. The goal of this workshop is to explore optimal problem-adapted approximation spaces, their theoretical properties, and their efficient computation. The use of problem-adapted approximation spaces is particularly advantageous in time-dependent or multi-query scenarios, such as statistical analysis, where multiscale constructions can be repeatedly applied to optimize the simulation at coarse scales. Participants will gain insight into recent advances in multiscale methods and have the opportunity to exchange ideas and collaborate with other workshop members and participants of the Junior Trimester Program.