Application of block Krylov subspace algorithms to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD

TL;DR

This paper demonstrates that a new block Krylov subspace algorithm significantly reduces computational costs in solving the Wilson-Dirac equation with multiple sources in lattice QCD, maintaining numerical accuracy.

Contribution

The authors introduce a novel block Krylov subspace algorithm tailored for the Wilson-Dirac equation with multiple right-hand sides, improving efficiency in lattice QCD calculations.

Findings

Reduces computational cost in lattice QCD simulations.

Maintains numerical accuracy with the new algorithm.

Applicable to the O(a)-improved Wilson-Dirac equation.

Abstract

It is well known that the block Krylov subspace solvers work efficiently for some cases of the solution of differential equations with multiple right-hand sides. In lattice QCD calculation of physical quantities on a given configuration demands us to solve the Dirac equation with multiple sources. We show that a new block Krylov subspace algorithm recently proposed by the authors reduces the computational cost significantly without loosing numerical accuracy for the solution of the O(a)-improved Wilson-Dirac equation.