A relaxed generalized-PSS preconditioner for saddle-point linear systems from steady incompressible Navier–Stokes equations

Abstract

We propose a relaxed generalized-PSS preconditioner for generalized saddle-point linear systems with non-Hermitian positive definite leading block from steady incompressible Navier–Stokes equations. The results indicate that the new preconditioner outperforms the existing variants of the PSS preconditioner in terms of the difference between the system matrix and the preconditioners, the eigenvalue distributions of the preconditioned system matrices, and computational complexities during the setup procedures and the preconditioning steps. The optimal-likelihood parameters selection strategy brings the new preconditioner into practical applications. Numerical examples demonstrate the effectiveness and robustness of the new preconditioner.