Accelerating iterative linear equation solver using modified domain-wall fermion matrix in lattice QCD simulations

TL;DR

This paper investigates how a variant of the domain-wall fermion operator can accelerate iterative solvers in lattice QCD simulations, demonstrating improved convergence and condition number analysis, with plans for code release.

Contribution

It introduces and evaluates a modified domain-wall operator that enhances solver efficiency in lattice QCD calculations.

Findings

Accelerated convergence of linear solvers with the modified operator

Improved condition number of the operator

Potential for GPU-accelerated lattice QCD simulations

Abstract

Lattice simulations of Quantum Chromodynamics (QCD) enable one to calculate the low-energy properties of the strong interaction among quarks and gluons based on the first principle. The most time-consuming part of the numerical simulations of lattice QCD is typically solving a linear equation for the quark matrix. In particular, a discretized quark formulation called the domain-wall fermion operator requires a high numerical cost, while retaining the lattice version of the chiral symmetry to good precision. The domain-wall operator is defined on a five-dimensional (5D) space extending the four-dimensional (4D) spacetime with an extra fifth coordinate. After solving the linear equation in 5D space, the result vector is projected onto the original 4D space. There is a variant of the domain-wall operator that improves the convergence of the 5D linear equation while unchanging the 4D solution vector. In this paper, we examine how this variant of the domain-wall operator accelerates the iterative linear equation solver in practical setups. We also measure the eigenvalues of the operator and compare the condition number with the convergence of the solver. We use a generic lattice QCD code set Bridge++ that is planned to be released including the improved form of the domain-wall operator examined in this work with code for the GPU.