Keywords: parallel computing, domain decomposition methods, Schwarz-type methods, asynchronous iterations, coarse-grid correction, non-blocking synchronization.

From the very beginning of parallel numerical computing, its major difficulty consists in achieving highly scaling solvers. This is due to its inherent synchronization phases, which are required after each iteration in traditional iterative computing. Asynchronous iterative computing early arose to overcome such a restriction, which makes it an attractive approach towards high performance computing. Nevertheless, asynchronous convergence is guaranteed so far for relaxation methods only, which do not provide the highest convergence rates in many situations. Efforts to achieve more competitive asynchronous solvers include their design within domain decomposition frameworks and, recently, with coarse-grid correction. We propose here a new formulation of asynchronous additive coarse-grid correction, which allows for convergence conditions independent of communications delays. Our approach is based on a two-splitting formulation of the two-level solver, leading to a hybrid synchronous-asynchronous method where asynchronous iterations are combined in parallel with synchronous ones. This possibly paves the way to asynchronous convergence acceleration using quite effective relaxation coefficients obtained from synchronized data.

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