Local Discontinuous Galerkin for the Functional Renormalisation Group

TL;DR

This paper introduces a Local Discontinuous Galerkin method for solving flow equations in the O(N)-model within the Local Potential Approximation, demonstrating improved stability and providing detailed implementation within a high-performance PDE framework.

Contribution

It presents a novel application of the Local Discontinuous Galerkin discretisation to the functional renormalisation group equations, with publicly available code and detailed implementation.

Findings

Enhanced numerical stability observed across various N and d

Successful implementation within the DUNE PDE framework

Open-source code available for further research

Abstract

We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various $N$ and space-time dimensions $d$. A particular focus of this work is the numerical discretisation and its implementation. The code is publicly available, and is explained in detail here. It is realised as a module within the high performance PDE framework DUNE.