Optimized Schwarz methods are very efficient iterative algorithms for the parallel solution of computational mechanics problems. These methods are similar to the classical Schwarz methods, but they use absorbing interface conditions between the sub-domains. These interface conditions are then optimized for efficiency and lead to a fast and robust convergence behavior of the iterative algorithm. A wide range of optimization techniques have been proposed and developed in the literature. In this chapter, optimized Schwarz methods are extended to the asynchronous context. The word asynchronous here is related to the iterations of the mathematical algorithm. Numerical experiments illustrate the robustness and efficiency of this original approach when solving the Helmholtz equation on parallel computers.
