Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs

TL;DR

This paper demonstrates how leveraging GPU computing significantly accelerates solving the ghost-gluon Dyson-Schwinger equations in Yang-Mills theory, enabling more efficient calculations for complex quantum field systems.

Contribution

The paper introduces a GPU-accelerated method for solving coupled integral equations in Yang-Mills theory, achieving two orders of magnitude speedup over traditional approaches.

Findings

GPU implementation reduces computation time by 100x

Parallelized Newton-Raphson method effectively solves non-linear equations

Feasibility of GPU-based Schwinger function calculations demonstrated

Abstract

We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.