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Thursday, Apr. 24, 9:30 am in MTH 3206, University of Maryland, College Park

Schwarz methods for saddle point problems (Stokes and linearized Navier-Stokes problems)

Prof. Luca Pavarino

Department of Mathematics, Universit\`a di Pavia, 27100 Pavia, ITALY

We introduce some parallel and scalable iterative methods for saddle point problems with a penalty term, such as the Stokes problem, the linearized Navier-Stokes equations and the mixed formulation of linear elasticity. These are domain decomposition methods of overlapping Schwarz type, based on the solution of local saddle point problems on overlapping subdomains and the solution of a coarse saddle point problem. The resulting indefinite preconditioner is accelerated by GMRES. Numerical experiments indicate that the rate of convergence of the preconditioned operator is independent of the mesh size, the number of subdomains and the penalty parameter.