On Constraint Preconditioners For A Class Of Special Saddle Point Problem

The coefficient matrix of a large and sparse saddle point linear systems arising from2D linearized Navier-Stokes equation is the type of block3×3. In2011, Benzi and Guo proposed a dimensional split(DS)preconditioner for these systems. In the same year, Benzi studied a relaxed dimensional factorization precondi-tioner(RDF) method to relax the rate of convergence of DS method. In2013, Cao and Yao pro-posed a modified dimensional split (MDS) preconditioner, In the same year, a relaxed modified dimensional factorization preconditioner to relax the rate of convergence of MDS method.In this paper, we study a large and sparse saddle point linear systems arising from2D linearized Navier-Stokes equation. In2002, Krukier studied the case that the skew-Hermitian part is greater Hermitian part and proposed his method, then MSTS method, PSTS method and MPSTS method were proposed one after another. Based on the above method, a class of new constraint precondetioners—GMPSTS method is introduced for the special linear system. The spectral properties of the preconditioned matrices and parameter choices are discussed. Moreover some spe-cial cases of the constraint preconditioners are given. Numerical experiments show that the new constraint preconditioners are feasible and effective, moreover it is more effective than MPSTS method.