Modified Block BiCGSTAB for Lattice QCD

TL;DR

This paper introduces a modified block BiCGSTAB algorithm with QR decomposition and SAP preconditioning, significantly improving efficiency in solving lattice QCD equations with multiple right-hand sides.

Contribution

The paper presents a novel combination of QR decomposition and SAP preconditioning within block BiCGSTAB for lattice QCD, enhancing convergence and reducing computational costs.

Findings

Improved convergence with QR decomposition

Reduced communication overhead with SAP preconditioner

Significant cost reduction through cache tuning and fewer iterations

Abstract

We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a $32^3 \times 64$ lattice at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.