On the semi-convergence of regularized HSS iteration methods for singular saddle point problems from the Stokes equations
For researchers solving singular saddle point problems from fluid dynamics, this provides a theoretically grounded iterative method with relaxed convergence requirements.
The paper extends the regularized HSS iteration method to singular saddle point problems from the Stokes equations, proving unconditional semi-convergence for both RHSS and HSS methods, which weakens previous convergence conditions. Numerical experiments demonstrate feasibility and effectiveness.
Recently, Bai and Benzi proposed a class of regularized Hermitian and skew-Hermitian splitting methods (RHSS) iteration methods for solving the nonsingular saddle point problem. In this paper, we apply this method to solve the singular saddle point problem from the Stokes equations. In the process of the semi-convergence analysis, we get that the RHSS method and the HSS method are unconditionally semi-convergent, which weaken the previous results. Then some spectral properties of the corresponding preconditioned matrix and a class of improved preconditioned matrix are analyzed. Finally, some numerical experiments on linear systems arising from the discretization of the Stokes equations are presented to illustrate the feasibility and effectiveness of this method and preconditioners.