Uzawa algorithms with variable relaxation for nonsymmetric generalized saddle point problems

作者：Shen, Hailun; Xiang, Hua^*

来源：Numerical Linear Algebra with Applications, 2015, 22(6): 1020-1038.

DOI：10.1002/nla.1988

• nonsymmetric
• saddle point problem
• Uzawa algorithm
• preconditioning

In this paper, we extend the inexact Uzawa algorithm of Hu and Zou to the nonsymmetric generalized saddle point problem (SPP). The techniques used here are similar with those in the paper of Bramble et al., where the convergence of Uzawa type algorithm for solving nonsymmetric case depends on the spectrum of the preconditioners involved. The main contributions of this paper focus on two new linear Uzawa type algorithms for nonsymmetric generalized saddle point problems and their convergence properties. Our exact Uzawa algorithm can always converge without any prior estimate on the spectrum of two preconditioned subsystems involved. The convergence of our inexact Uzawa algorithm does not need the prior spectrum estimate of Schur complement, which may not be easy to achieve in practical applications. Numerical results of the algorithm on the Navier-Stokes problem are also presented.

• 单位
  武汉大学