We introduce some parallel and scalable iterative methods for saddle-point problems with a penalty term, such as the mixed formulation of linear elasticity, the Stokes problem, and the linearized Navier-Stokes equations. 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 a Krylov space method such as 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.
Connect With Us: