Hierarchical Parallelisation of Functional Renormalisation Group Calculations -- hp-fRG

TL;DR

This paper demonstrates a multi-level parallelisation strategy for the functional renormalisation group method, significantly enhancing computational efficiency and enabling applications previously limited by high numerical costs.

Contribution

The work introduces a hierarchical parallelisation approach combining MPI, OpenMP, and SIMD, which drastically accelerates fRG calculations with minimal code modifications.

Findings

Code speed-up by several orders of magnitude

Successful application on two different HPC platforms

Moderate code changes enable large performance gains

Abstract

The functional renormalisation group (fRG) has evolved into a versatile tool in condensed matter theory for studying important aspects of correlated electron systems. Practical applications of the method often involve a high numerical effort, motivating the question in how far High Performance Computing (HPC) can leverage the approach. In this work we report on a multi-level parallelisation of the underlying computational machinery and show that this can speed up the code by several orders of magnitude. This in turn can extend the applicability of the method to otherwise inaccessible cases. We exploit three levels of parallelisation: Distributed computing by means of Message Passing (MPI), shared-memory computing using OpenMP, and vectorisation by means of SIMD units (single-instruction-multiple-data). Results are provided for two distinct High Performance Computing (HPC) platforms, namely the IBM-based BlueGene/Q system JUQUEEN and an Intel Sandy-Bridge-based development cluster. We discuss how certain issues and obstacles were overcome in the course of adapting the code. Most importantly, we conclude that this vast improvement can actually be accomplished by introducing only moderate changes to the code, such that this strategy may serve as a guideline for other researcher to likewise improve the efficiency of their codes.