Protocol-free asynchronous iterations termination

In this paper, we tackled the convergence detection problem arisen from the absence of synchronization during asynchronous iterative computation. We showed that, when one arbitrarily takes the local components of a global solution vector, an upper bound can be established on the difference between a residual error evaluated from this global vector and the inconsistent residual error evaluated without synchronizing the involved computing processes. This allows for accurate termination of asynchronous iterations without implementing any particular detection protocol. Termination delay has be handled too for not slowing down the overall asynchronous solver, by appropriately setting the convergence threshold criterion. We therefore ensured effectiveness while reaching better efficiency in terms of overall execution time of the solver, in comparison with the current most efficient exact snapshot-based approach. © 2020 Elsevier Ltd