HMC algorithm for two-flavour lattice QCD: Schwarz-preconditioning with a one-dimensional domain decomposition

TL;DR

This paper introduces a simplified Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD, applying domain decomposition in one dimension to improve computational efficiency and reduce the fermion matrix condition number.

Contribution

The paper presents a novel one-dimensional domain decomposition approach within Schwarz-preconditioned HMC, demonstrating its effectiveness for two-flavour Wilson fermions.

Findings

Reduced condition number of fermion matrix

Improved computational performance over previous methods

Feasibility of iterative domain decomposition

Abstract

We study a variant of the Schwarz-preconditioned HMC algorithm. In contrast to the original proposal of L\"uscher, we apply the domain decomposition in one lattice direction only. This is sufficient to reduce the condition number of the fermion matrix restricted to the domains compared with the full fermion matrix. For the same linear extension of the domain, less links reside on the boundaries of the domains. Therefore it becomes e.g. practical to iterate the decomposition. We perform numerical tests for two degenerate flavours of Wilson fermions. The standard Wilson gauge action at $\beta=5.6$ is used. The performance of our implementation is compared with other recent studies using various types of preconditioning.