Overlapping Schwarz preconditioners for spectral element discretizations of convection-diffusion problems

The classical overlapping Schwarz algorithm is here extended to stabilized spectral element discretizations of convection-di3usion problems. The algorithm solves iteratively the resulting non-symmetric system of linear equations by a preconditioned GMRES method. The preconditioner is built from local convection-di3usion solvers on overlapping subdomains and from a coarse convection-di3usion solver on a coarse mesh de;ned by the subdomain boundaries. Several numerical experiments on test problems in the plane indicate that this algorithm retains the fast convergence rate and optimal scalability properties of classical overlapping methods for di3usion dominated problems. Fast convergence is also obtained for convection dominated problems without closed streamlines and with a moderate number of subdomains