An investigation into a wavelet accelerated gauge fixing algorithm

TL;DR

This paper presents a wavelet-based acceleration algorithm for gauge fixing in lattice gauge theory, demonstrating significant iteration reduction compared to unaccelerated methods, with potential improvements over Fourier acceleration.

Contribution

It introduces a novel wavelet acceleration method for gauge fixing, showing it can reduce iterations more efficiently than traditional Fourier acceleration.

Findings

Wavelet acceleration reduces iterations by up to 3 times.

The method outperforms unaccelerated algorithms.

Results are demonstrated on $SU(3)$ on $8^{4}$ lattices.

Abstract

We introduce an acceleration algorithm for coulomb gauge fixing, using the compactly supported wavelets introduced by Daubechies. The algorithm is similar to Fourier acceleration. Our provisional numerical results for $SU(3)$ on $8^{4}$ lattices show that the acceleration based on the DAUB6 transform can reduce the number of iterations by a factor up to 3 over the unaccelerated algorithm. The reduction in iterations for Fourier acceleration is approximately a factor of 7.