Solution of the Dirac equation in lattice QCD using a domain decomposition method

TL;DR

This paper demonstrates that domain decomposition methods, specifically Schwarz preconditioners, significantly improve the efficiency of solving the Wilson-Dirac equation in lattice QCD on parallel computers by reducing communication overhead.

Contribution

It introduces an effective domain decomposition approach combined with Krylov solvers for the Wilson-Dirac equation, enhancing parallel efficiency in lattice QCD computations.

Findings

Reduced communication overhead with Schwarz preconditioners

Improved scalability over even-odd preconditioned solvers

Effective distribution of computational work across processors

Abstract

Efficient algorithms for the solution of partial differential equations on parallel computers are often based on domain decomposition methods. Schwarz preconditioners combined with standard Krylov space solvers are widely used in this context, and such a combination is shown here to perform very well in the case of the Wilson--Dirac equation in lattice QCD. In particular, with respect to even-odd preconditioned solvers, the communication overhead is significantly reduced, which allows the computational work to be distributed over a large number of processors with only small parallelization losses.