A BFBt preconditioner for Double Saddle-Point Systems

TL;DR

This paper develops a variant of the BFBt preconditioner tailored for double saddle-point systems, analyzing its spectral properties and demonstrating effectiveness on Stokes-Darcy discretizations.

Contribution

It introduces a new BFBt-based preconditioner for double saddle-point systems and studies its eigenvalue distribution and performance.

Findings

Improved eigenvalue clustering for the preconditioned system

Enhanced convergence in Stokes-Darcy simulations

Effective approximation of the nested Schur complement

Abstract

We consider block preconditioners for double saddle-point systems, and investigate the effect of approximating the nested Schur complement associated with the trailing diagonal block on the eigenvalue distribution of the preconditioned matrix. We develop a variant of Elman's BFBt method and adapt it to this family of linear systems. Our findings are illustrated on a Marker-and-Cell discretization of the Stokes-Darcy equations.