Termine Angewandte Mathematik Münster

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.