Asynchronous Additive Coarse-Space Correction

Data access time is an essential part of the mathematical design of asynchronous iterative methods, which makes it necessary to strongly link theoretical analysis and practical implementation. In particular, coarse-space correction implies two independent communications stages, one for updating the right-hand side (RHS) of each local fine problem, and the other one for updating the RHS of the coarse problem. This results in two different sets of communication delays, creating a gap between the fine- and the coarse-projected RHSs. So far, asynchronous domain decomposition methods (DDMs) have applied additive coarse-space correction only on a subset of iterations, depending on the average gap between the RHSs. Here, we achieve asynchronous additive coarse-space correction at all iterations and hence propose the first totally two-level asynchronous DDMs of such kind. The approach is presented using a general Schwarz-type domain decomposition framework formulated as a multisplitting one. Several iterative models are considered with implied implementation aspects. Both weak and strong scaling experimental results for the standard Poisson’s equation in two and three dimensions show some remarkable performances of our approach.