Emile Parolin: Thursday, 03rd July 2025 at 10:30
Abstract:
Efficiently solving partial differential equation problems with highly heterogeneous coefficients is challenging due to the need for fine meshes, leading to large-scale and ill-conditioned linear systems. Domain decomposition methods address this by constructing efficient preconditioners that solve independent local problems in parallel. A key aspect to achieve scalability and robustness in these methods is the incorporation of a suitable coarse space.
This presentation begins with an overview of one-level preconditioners, then introduces a novel algebraic construction of adaptive coarse spaces for two-level methods. The analysis is broadly applicable, encompassing non-hermitian and indefinite problems, as well as symmetric preconditioners like the additive Schwarz method and non-symmetric ones such as the restricted additive Schwarz method. It can also account for both exact and inexact subdomain solves. The coarse space is constructed by solving local generalized eigenproblems within each subdomain and applying a carefully chosen operator to the selected eigenvectors to obtain a local discrete solution.
This is based on a joint work with Frédéric Nataf and Pierre-Henri Tournier.
