Relaxed block upper–lower triangular preconditioner for generalized saddle point problems from the incompressible Navier–Stokes equations

Abstract

Based on a new matrix splitting of the original coefficient matrix, a relaxed block upper–lower triangular (RBULT) preconditioner is proposed for the solution of generalized saddle point problem arising from the incompressible Navier–Stokes equations. The distinct advantage of this preconditioner is that it is computationally cheaper to implement than the modified dimensional split (MDS) preconditioner, the generalized relaxed splitting (GRS) preconditioner, and the modified relaxed splitting (MRS) preconditioner when using Krylov subspace methods. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are given. Finally, numerical results are provided to demonstrate the validity of the theoretical analysis, which indicate not only that the RBULT preconditioner is competitive when compared with other state-of-the-art preconditioners, but that it is more effective.