Abstract
Based on the block triangular splitting of the original coefficient matrix, a relaxed upper and lower triangular splitting (RULT) preconditioner for the linearized incompressible Navier–Stokes equations is considered. The convergence analysis of the RULT iteration method is presented. The spectral properties and the degrees of the minimal polynomials of the preconditioned matrices are discussed, respectively. Then the quasi-optimal parameters of the RULT preconditioner are derived. Finally, some numerical results are carried out to show the effectiveness of the RULT preconditioner, and verify that the RULT preconditioner outperforms the MDS, GRS, MRS and RBTS preconditioners for the GMRES method for solving the linearized incompressible Navier–Stokes equation in terms of the number of iterations and computation times.
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