Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized Biconjugate Gradient Algorithm

TL;DR

This paper evaluates the BiCGStab algorithm for inverting Wilson fermion matrices in lattice QCD, demonstrating its superior efficiency over traditional methods, especially at small quark masses.

Contribution

It applies and compares the BiCGStab algorithm to existing methods for lattice fermion matrix inversion, showing its advantages in computational efficiency.

Findings

BiCGStab outperforms conjugate gradient and minimal residual methods.

BiCGStab is particularly effective in the chiral regime with small quark masses.

The method is tested on both quenched and dynamical gauge configurations.

Abstract

The stabilized biconjugate gradient algorithm BiCGStab recently presented by van der Vorst is applied to the inversion of the lattice fermion operator in the Wilson formulation of lattice Quantum Chromodynamics. Its computational efficiency is tested in a comparative study against the conjugate gradient and minimal residual methods. Both for quenched gauge configurations at beta= 6.0 and gauge configurations with dynamical fermions at beta=5.4, we find BiCGStab to be superior to the other methods. BiCGStab turns out to be particularly useful in the chiral regime of small quark masses.