Coarse space preconditioning for Generalized Optimized Schwarz Methods. Part I: continuous case

Abstract

The Generalized Optimized Schwarz Method (GOSM) originally proposed in [Claeys, 2021] is a variant of Depr\'es algorithm, a domain decomposition strategy for the solution of harmonic wave propagation problems. It imposes transmission conditions through interfaces by means of a non-local exchange operator. Conducting our analysis at the continuous level, in an infinite dimensional setting, we propose a coarse space construction for the preconditioning of the GOSM formulation, and provide estimates for the convergence of GMRes applied to the preconditioned equation.