Variants of the PSS preconditioner for generalized saddle point problems from the Navier-Stokes equations

TL;DR

This paper introduces new matrix-splitting preconditioners for generalized saddle-point systems, improving convergence and spectrum properties, especially for singular and rank-deficient cases, demonstrated through numerical experiments.

Contribution

It proposes novel preconditioner variants that extend existing methods to more general saddle-point problems with singular and rank-deficient blocks.

Findings

Better convergence properties compared to existing preconditioners

Improved spectrum distribution for the new preconditioners

Numerical experiments confirm efficiency and robustness

Abstract

In this paper, a class of new preconditioners based on matrix splitting are presented for generalized saddle-point linear systems, which can be viewed as further modified improvements of some recently published preconditioners. Moreover, we widen the scope of the new preconditioners to solve the more general but rarely considered saddle-point linear systems with singular leading blocks and rank-deficient off-diagonal blocks. The new variants can result in much better convergence properties and spectrum distributions than the original existing preconditioners. Numerical experiments are used to illustrate the efficiency of the new proposed preconditioners.