Résumé : I will present an efficient implementation of the highly robust and scalable GenEO preconditioner in the high-performance PDE framework DUNE. The GenEO coarse space is constructed by combining low energy solutions of local generalised eigenproblems using a partition of unity. In this talk, both weak and strong scaling for the GenEO solver on over 15,000 cores will be demonstrated by solving an industrially motivated problem with over 200 million degrees of freedom in aerospace composites modelling. Further, it will be shown that for highly complex parameter distributions in certain real-world applications, established methods can become intractable while GenEO remains fully effective. In the context of multilevel Markov chain Monte Carlo (MLMCMC), the GenEO coarse space also plays an important role as an effective surrogate model in PDE-constrained Bayesian inference. The second part will therefore focus on the approximation properties of the GenEO coarse space and on a high-performance parallel implementation of MLMCMC.
This is joint work with Tim Dodwell (Exeter), Anne Reinarz (TU Munich) and Linus Seelinger (Heidelberg).

Keywords : generalised finite elements; multiscale methods; domain decomposition; strong coefficient variation; anisotropic linear elasticity; parallel scaling