An Improved Uzawa-PSS Method for to Solve Point Problems

doi:10.12068/j.issn.1005-3026.2019.05.028

Abstract

Abstract: Aiming at the non-Hermitian saddle point problem， an improved Uzawa-PSS iteration method is constructed based on the existing Uzawa-PSS method. The main idea of the new method is to solve two linear subsystems in each iteration step of Uzawa-PSS method， whose coefficient matrices are αI+P and αI+S， respectively. The first subsystem can be solved by CG method， but the second subsystem is very difficult to solve. The improved algorithm uses the single-step PSS iteration method to approximate the problem. Then the new method is used to solve the non-singular and singular saddle point problems respectively， and the corresponding convergence analysis is given. The numerical simulation also proves that the improved Uzawa-PSS iteration method has obvious advantages in iteration steps， CPU time and relative residuals.

Key words: saddle point problem, convergence, semi-convergence, singular, nonsingular

CLC Number:

O241.6

SHEN Hai-long， LI Hong-li， SHAO Xin-hui. An Improved Uzawa-PSS Method for to Solve Point Problems[J]. Journal of Northeastern University Natural Science, 2019, 40(5): 756-760.

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