Single flavour optimisations to Hybrid Monte Carlo

Abstract

It has become increasingly important to include one or more individual flavours of dynamical fermion in lattice QCD simulations. This is due in part to the advent of QCD+QED calculations, where isospin symmetry breaking means that the up, down, and strange quarks must be treated separately. These single-flavour pseudofermions are typically implemented as rational approximations to the inverse of the fermion matrix, using the technique known as Rational Hybrid Monte Carlo (RHMC). Over the years, a wide range of methods have been developed for accelerating simulations of two degenerate flavours of pseudofermion, while there are comparatively fewer such techniques for single-flavour pseudofermions. Here, we investigate two different filtering methods that can be applied to RHMC for simulating single-flavour pseudofermions, namely polynomial filtering (PF-RHMC), and filtering via truncations of the ordered product (tRHMC). A novel integration step-size tuning technique based on the characteristic scale is also introduced. Studies are performed on two different lattice volumes, demonstrating that one can achieve significant reductions in the computational cost of single-flavour simulations with these filtering techniques.

State mixing and masses of the $π^0$, $η$ and $η^\prime$ mesons from $n_f=1+1+1$ lattice QCD+QED

“…(2) (21) which clearly agree within their uncertainties. We hence drop the smearing index l from our re-scaled operators Eq.…”

“…We would like to thank A. Hannaford-Gunn for their helpful feedback and discussion during the preparation of this manuscript. The numerical configuration generation (using the BQCD lattice QCD program [20] with single quark flavours treated in the HMC by the tRHMC algorithm [21]) and data analysis (using the Chroma software library [22] and a GPU-accelerated mixed-precision conjugate gradient fermion matrix inverter through the COLA software [23]) was carried out on the DiRAC Blue Gene Q and Extreme Scaling (EPCC, Edinburgh, UK) and Data Intensive (Cambridge, UK) services, the GCS supercomputers JUQUEEN and JUWELS (NIC, Jülich, Germany) and resources provided by HLRN (The North-German Supercomputer Alliance), the NCI National Facility in Canberra, Australia (supported by the Australian Commonwealth Government) and the Phoenix HPC service (University of Adelaide…”

Evolving the COLA software library

“…Key algorithms are solvers for linear systems and eigenmodes [1], and gauge field generation with Hybrid Monte Carlo [2]. The latter features a number of variants such as the RHMC algorithm [3] and a selection of filtering techniques [4][5][6]. Specific physics features are tailored to the CSSM lattice research programme, for which the COLA software library has formed the computational foundation for some time .…”