Optimized implementation of the conjugate gradient algorithm for FPGA-based platforms using the Dirac-Wilson operator as an example

TL;DR

This paper presents an optimized FPGA implementation of the Conjugate Gradient algorithm tailored for the Dirac-Wilson operator, enhancing performance for scientific computations in Quantum Chromodynamics on heterogeneous systems.

Contribution

It introduces a flexible, high-performance FPGA-based software package for the Conjugate Gradient algorithm, optimized for the Dirac-Wilson operator, with adaptable data transport mechanisms.

Findings

Achieved maximal performance with FPGA implementation

Framework allows easy adaptation to other linear operators

Facilitates porting of iterative solvers to FPGA platforms

Abstract

It is now a noticeable trend in High Performance Computing that the systems are becoming more and more heterogeneous. Compute nodes with a host CPU are being equipped with accelerators, the latter being a GPU or FPGA cards or both. In many cases at the heart of scientific applications running on such systems are iterative linear solvers. In this work we present a software package which includes an FPGA implementation of the Conjugate Gradient algorithm using a particular problem of the Dirac-Wilson operator as encountered in numerical simulations of Quantum Chromodynamics. The software is written in OpenCL and C++ and is optimized for maximal performance. Our framework allows for a simple implementation of other linear operators, while keeping the data transport mechanisms unaltered. Hence, our software can serve as a backbone for many applications which are expected to gain a significant boost factor on FPGA accelerators. As such systems are expected to become more and more widespread, the need for highly performant FPGA implementations of the Conjugate Gradient algorithm and its variants will certainly increase and the porting investment can be greatly facilitated by the attached code.