Termine

Further information

This talk presents a generalised framework for coupling various discretisation methods for fluid problems using domain decomposition (DD) algorithms. In the first part, I will introduce the optimisation-based DD approach, which ensures physical consistency across domains. We will explore optimal control formulations and briefly examine the analysis of the resulting decoupled system, highlighting efficient numerical optimisation techniques that enable parallelisation. Building on this, we will discuss the construction of localised domain-decomposed Reduced Order Models (ROMs) and the heterogeneous coupling of high-fidelity and low-fidelity models within this optimisation-based framework.
The second part of the talk will focus on extending this methodology to multiphysics problems, particularly fluid-structure interaction (FSI). Given the complexity of FSI problems and the need for small time steps to ensure numerical convergence, we will explore initial attempts to incorporate time adaptivity into the domain-decomposed model order reduction framework. This requires more effective optimisation algorithms to overcome the slow, local convergence of classical minimisation methods. In particular, we will discuss a trust-region approach to address this challenge and get a look at the preliminary numerical results.
The seminar will conclude with open questions and future research directions, including ongoing endeavours in the development of efficient multi-domain decomposition techniques.

New postdocs of Mathematics Münster will introduce themselves at the MM Postdoc Colloquium. In short lectures they will give an insight into their fields of research and outlined the research questions they will be dealing with in Münster.

• Gayrat Toshpulatov -- Long time behavior of kinetic equations
• Dario Reggiani -- Gamma-convergence and stochastic homogenisation of degenerate functionals
• Francesco Deangelis -- Homogenization on randomly perforated domains
• Floris Vermeulen -- Definable sets in valued fields
• Ioannis Zachos -- On semi-stable integral models for some Shimura varieties
• Sam Shepherd -- Quasi-isometric rigidity of groups

A hypersurface of a Lorentzian manifold is called null, if its induced metric is degenerate. In such geometries, classical some geometric concepts are unavailable and for this reason there is little knowledge about curvature flows in such spaces. Building upon a definition of mean curvature flow I developed with Henri Roesch few years ago, we extend and improve the analysis to constrained mean curvature flows, which will then enable us to foliate large classes of null hypersurfaces by surfaces of constant spacetime mean curvature. This is joint work with Wilhelm Klingenberg (Durham) and Ben Lambert (Leeds).