Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier-Stokes equations

TL;DR

This paper demonstrates that Anderson-accelerated Newton's method converges superlinearly for stationary Navier-Stokes equations, with convergence speed influenced by Anderson depth, and shows that acceleration can extend the convergence domain.

Contribution

It provides theoretical and numerical evidence that Anderson acceleration enhances Newton's method for Navier-Stokes equations, including convergence rate and domain of convergence improvements.

Findings

Superlinear convergence with good initial guess.

Large Anderson depth slows convergence.

Acceleration can enlarge convergence domain.

Abstract

This paper studies the performance Newton's iteration applied with Anderson acceleration for solving the incompressible steady Navier-Stokes equations. We manifest that this method converges superlinearly with a good initial guess, and moreover, a large Anderson depth decelerates the convergence speed comparing to a small Anderson depth. We observe that the numerical tests confirm these analytical convergence results, and in addition, Anderson acceleration sometimes enlarges the domain of convergence for Newton's method.