Efficient HSS-based preconditioners for generalized saddle point problems

A fast iteration method based on HSS is proposed for solving the nonsymmetric generalized saddle point problem. It converges to the unique solution of the generalized saddle point problem unconditionally. We devise a new preconditioner induced by the new iteration method. We analyze the spectrum of the preconditioned coefficient matrix, and reveal the relation between the theoretically required number of iteration steps and the dimension of the preconditioned Krylov subspace. Furthermore, some practical inexact variants of the new preconditioner have been developed to reduce the computational overhead. Numerical experiments validate the effectiveness of the proposed preconditioners.