Application of preconditioned block BiCGGR to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD

TL;DR

This paper improves the convergence of block BiCGGR method for solving the Wilson-Dirac equation with multiple right-hand sides in lattice QCD by introducing a preconditioning technique, addressing previous issues of residual deviation and convergence failure.

Contribution

The authors demonstrate that preconditioning enhances the convergence of block BiCGGR for multiple right-hand sides in lattice QCD, building on their recent algorithm.

Findings

Preconditioning improves convergence for multiple right-hand sides.

The method addresses residual deviation issues.

Enhanced stability at smaller quark masses.

Abstract

There exist two major problems in application of the conventional block BiCGSTAB method to the O(a)-improved Wilson-Dirac equation with multiple right-hand-sides: One is the deviation between the true and the recursive residuals. The other is the convergence failure observed at smaller quark masses for enlarged number of the right-hand-sides. The block BiCGGR algorithm which was recently proposed by the authors succeeds in solving the former problem. In this article we show that a preconditioning technique allows us to improve the convergence behavior for increasing number of the right-hand-sides.