Appears in collection : Jean-Morlet Chair 2022: Research School - Domain Decomposition for Optimal Control Problems / Chaire Jean-Morlet 2022 - Ecole - Décomposition des domaines pour des problèmes de contrôle optimal

Domain decomposition methods are meant to be used as parallel solvers and scalability (behaviour independent of the number of subdomains/processors) and robustness with respect to the physical parameters are very important issues. An introduction to coarse spaces and two-level methods for symmetric positive definite (SPD) problems will be given together with the presentation of a few variants of domain decomposition preconditioners (AS, RAS, ORAS, SORAS). The content will follow chapters 4 and 5 from the book, although more recent research results will also be included. Outcomes: Students will be able to understand the use and the impact of the two-level methods both for scalability and robustness (even if at this stage the codes are sequential).