We develop a finite element based additive Schwarz preconditioner for the spectral element formulation of the incompressible Navier-Stokes equations. The importance of the coarse grid solve in this context is demonstrated, and an efficient (direct) parallel coarse grid solver is presented which is particularly suited to large numbers of processors. For large two-dimensional problems this overlapping Schwarz approach can yield as much as a five-fold reduction in Navier-Stokes simulation time over previously employed methods based upon deflation.

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1996-1997 Mathematics in High Performance Computing