Accurate implementation of two-level asynchronous domain decomposition solvers

Abstract

Recently, asynchronous coarse-grid correction has been achieved within additive Schwarz-type and primal Schur domain decomposition frameworks. Both additive and multiplicative coarse-grid corrections were discussed, however, the implemented asynchronous Schwarz-type solver with additive correction relies on the specific design of the restricted additive Schwarz (RAS) method, and also requires an overlap between the subsets of unknowns. In this paper, we first highlight a gap between the theoretical analysis from the literature and the associated RAS implementation. It turns out that communications delays would actually need to be bounded in order to fit the theory. This has to be stressed since, despite the asynchronous nature of the solver, the coarse-grid correction requires non-blocking global synchronization, which is subject to communications bottleneck. Second, we propose an implementation approach which applies to a wider class of additive Schwarz-type methods while still coping with the bounded delays requirement.