A multigrid implementation of the Fourier acceleration method for Landau gauge fixing

TL;DR

This paper introduces a multigrid-based Fourier acceleration method for Landau gauge fixing that avoids FFT, enhances flexibility, and demonstrates excellent parallel scalability on high-performance computing architectures.

Contribution

The paper presents a novel multigrid implementation of Fourier acceleration for Landau gauge fixing, improving flexibility and parallel efficiency over traditional FFT-based methods.

Findings

Equivalent performance to standard Fourier acceleration on serial machines

Linear speedup achieved with increasing processors on parallel machines

Conjugate gradient variant effective at intermediate lattice volumes

Abstract

We present a new implementation of the Fourier acceleration method for Landau gauge fixing. By means of a multigrid inversion we are able to avoid the use of the fast Fourier transform. This makes the method more flexible, and well suited for vector and parallel machines. We study the performance of this algorithm on serial and on parallel (APE100) machines for the 4-dimensional SU(2) case. We find that our method is equivalent to the standard implementation of Fourier acceleration already on a serial machine, and that it parallelizes very efficiently: its computational cost shows a linear speedup with the number of processors. We have also implemented, on the parallel machines, a version of the method using conjugate gradient instead of multigrid. This leads to an algorithm that is efficient at intermediate lattice volumes.