A modified dimensional split preconditioner for generalized saddle point problems

Abstract

For large and sparse saddle point linear systems arising from 2D linearized Navier–Stokes equations, Benzi and Guo recently studied a dimensional split (DS) preconditioner (Appl. Numer. Math. 61 (2011) 66–76). By further applying it to generalized saddle point problems, in this paper we present a modified dimensional split (MDS) preconditioner. This new preconditioner is based on a splitting of the generalized saddle point matrix, resulting in an unconditional convergent fixed-point iteration. The basic iteration is accelerated by a Krylov subspace method like restarted GMRES. The implementation of the MDS preconditioner is discussed and a similar case is also analyzed. Finally, numerical experiments of a model Navier–Stokes problem are presented to illustrate the effectiveness of the MDS preconditioner.