Numerical experiments have shown that Schwarz preconditioning improves significantly the GMRES convergence for different values of physical and numerical parameters, and that the ORAS preconditioner always performs much better than the OAS preconditioner. The only advantage of the OAS method is to preserve the symmetry of the preconditioner. Finally, it has been pointed out that the spectrum of the preconditioned matrix reflects the convergence qualities, which improve when the eigenvalues are well clustered inside the unitary disk centered at (1,0).
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