A conforming auxiliary space preconditioner for the mass conserving mixed stress method

TL;DR

This paper introduces an auxiliary space preconditioner for the mass conserving mixed stress method applied to Stokes equations, enhancing the efficiency of solving the resulting linear systems through scalable solvers and static condensation.

Contribution

It develops a novel auxiliary space preconditioner tailored for the MCS method, focusing on polynomial degree scalability and efficient solution of pressure-velocity systems.

Findings

Preconditioner improves solver efficiency for MCS discretizations.

Numerical experiments confirm the scalability and effectiveness of the approach.

Implementation demonstrates potential for large-scale Stokes problem solutions.

Abstract

We are studying the efficient solution of the system of linear equation stemming from the mass conserving mixed stress (MCS) method discretization of the Stokes equations. To that end we perform static condensation to arrive at a system for the pressure and velocity unknowns. An auxiliary space preconditioner for the positive definite velocity block makes use of efficient and scalable solvers for conforming Finite Element spaces of low order and is analyzed with emphasis placed on the polynomial degree of the discretization. Numerical experiments demonstrate the potential of this approach and the efficiency of the implementation.