The Optimized Schwarz Method with a Coarse Grid Correction

Optimized Schwarz Methods (OSM) use Robin transmission conditions across the subdomain interfaces. The Robin parameter can then be optimized to obtain the fastest convergence. A new formulation is presented with a coarse grid correction. The optimal parameter is computed for a model problem on a cylinder, together with the corresponding convergence factor which is smaller than that of classical Schwarz methods. A new coarse space is presented, suitable for OSM. Numerical experiments illustrating the effectiveness of OSM with a coarse grid correction, both as an iteration and as a preconditioner, are reported.