一类广义鞍点问题的分裂预处理

A Splitting Preconditioner for Generalized Saddle Point Problems

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.

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.