An augmented Lagrangian-based preconditioning technique for a class of block three-by-three linear systems

TL;DR

This paper introduces an augmented Lagrangian preconditioner designed to improve the convergence of Krylov methods for complex block three-by-three linear systems from coupled flow problems, with demonstrated efficiency in 3D simulations.

Contribution

The paper presents a novel augmented Lagrangian-based preconditioning technique specifically for block three-by-three systems from coupled flow discretizations, enhancing solver performance.

Findings

Effective acceleration of Krylov methods demonstrated

Preconditioner shows good spectral properties

Numerical results confirm improved convergence

Abstract

We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element discretizations of the coupled Stokes-Darcy flow problem. We analyze the spectrum of the preconditioned matrix and we show how the new preconditioner can be efficiently applied. Numerical experiments are reported to illustrate the effectiveness of the preconditioner in conjunction with flexible GMRES for solving linear systems of equations arising from a 3D test problem.