Section: New Results

SORAS GenEO-2

Optimized Schwarz methods (OSM) are very popular methods which were introduced by P.L. Lions (1989) for elliptic problems and by B. Després (1990) for propagative wave phenomena. We (R. Haferssas, P. Jolivet and F. Nataf) give here a theory for Lions' algorithm that is the genuine counterpart of the theory developed over the years for the Schwarz algorithm. The first step is to introduce a new symmetric variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm that is suitable for the analysis of a two-level method. Then we build a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We show scalability results for thousands of cores for nearly incompressible elasticity and the Stokes systems with a continuous discretization of the pressure.