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.

基于原始系数矩阵的块三角分裂，考虑了线性不可压缩的Navier–Stokes方程的松弛上下三角分裂（RULT）预调节器。给出了RULT迭代方法的收敛性分析。分别讨论了预处理矩阵的光谱性质和最小多项式的次数。然后推导RULT预处理器的准最佳参数。最后，通过一些数值结果证明了RULT预调理器的有效性，并验证了RULT预调理器在GMRES方法求解线性化不可压缩Navier–Stokes方程方面优于MDS，GRS，MRS和RBTS预调理器。迭代次数和计算时间。