一类广义鞍点问题的分裂预处理

A Splitting Preconditioner for Generalized Saddle Point Problems

摘要

摘要:对于广义鞍点问题,基于参数化的Uzawa方法提出了一种新的预处理子,通过分析预处理后的系统,发现当参数t→0时,其特征值将集中到0和1,因此,当在Krylov子空间中使用某些GMRES迭代方法时,它将保证较好的收敛性.最后,运用Navier-Stokes方程中的一些例子进行实验,验证了这个预处理子的实际效果.

Abstract:Based on the parameterized Uzawa methods, a new preconditioner for generalized saddle point problems is worked out. An analysis of the pretreated matrix finds that the eigenvalues of the preconditioned matrix will cluster about 0 and 1 when the parameter t → 0. Consequently, on the condition of the proper selection of a parameter, it can ensure a satisfactory convergence when some GMRES iterative methods are used in Krylov subspace. Numerical results of some Navier-Stokes problems are presented to illustrate the actual effect of the preconditioner.