Accelerating the Uzawa Algorithm

TL;DR

This paper investigates the use of Anderson acceleration to enhance the convergence speed of the Uzawa algorithm for saddle-point problems, demonstrating significant improvements in fluid dynamics applications.

Contribution

It introduces Anderson acceleration to the Uzawa algorithm and compares its performance with other iterative methods on flow problems.

Findings

Accelerated Uzawa converges faster than the standard version.

The accelerated method is competitive with other iterative solvers.

Performance improvements are demonstrated on steady Stokes and Oseen problems.

Abstract

The Uzawa algorithm is an iterative method for the solution of saddle-point problems, which arise in many applications, including fluid dynamics. Viewing the Uzawa algorithm as a fixed- point iteration, we explore the use of Anderson acceleration (also known as Anderson mixing) to improve the convergence. We compare the performance of the preconditioned Uzawa algorithm with and without acceleration on several steady Stokes and Oseen problems for incompressible flows. For perspective, we include in our comparison several other iterative methods that have appeared in the literature. The results indicate that the accelerated preconditioned Uzawa algorithm converges significantly faster than the algorithm without acceleration and is competitive with the other methods considered.