On PSS-based constraint preconditioners for singular nonsymmetric saddle point problems

Abstract

For singular nonsymmetric saddle point problems, a class of singular constraint preconditioners and the corresponding preconditioning iteration methods are proposed based on the positive-definite and skew-symmetric splitting (PSS) of (1,1) block of the coefficient matrix, which can be categorized into a recently proposed generalized constraint preconditioner (GCP) for singular nonsymmetric saddle point problems. The convergence analysis of the preconditioned iteration method is presented and the convergence conditions are derived. Some numerical experiments are implemented to demonstrate the feasibility and effectiveness of the PSS-based constraint preconditioning both as a preconditioned iteration method and a preconditioner of the Krylov subspace method.