On HSS-based sequential two-stage method for non-Hermitian saddle point problems

For large sparse saddle point problems with symmetric positive definite (1, 1)-block, Li et al. studied an efficient iterative method (see Li et al. (2011)) [25]. By making use of the same preconditioning technique and a new matrix splitting based on the Hermitian and skew-Hermitian splitting (HSS) of the (1, 1)-block of the preconditioned non-Hermitian saddle point systems, an efficient sequential two-stage method is proposed for solving the non-Hermitian saddle point problems. Theoretical analysis shows the proposed iterative method is convergent, and that the spectral radius of iterative matrix monotonically decreases and tends to 0 as the iterative parameter αα approaches infinity. Numerical experiments arising from Naiver–Stokes problem are provided to show that the new iterative method is feasible, effective and robust.