Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs

Abstract

A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve maximum performance. In this work we concentrate on applications for lattice gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. We employ the overrelaxation, stochastic relaxation and simulated annealing algorithms which are perfectly suited to be accelerated by highly parallel architectures like GPUs. The applications support the Coulomb, Landau and maximally Abelian gauges. Moreover, we explore the evolution of the numerical accuracy of the SU(3) valued degrees of freedom over the runtime of the algorithms in single (SP) and double precision (DP). Therefrom we draw conclusions on the reliability of SP and DP simulations and suggest a mixed precision scheme that performs the critical parts of the algorithm in full DP while retaining 80-90% of the SP performance. Finally, multi-GPUs are adopted to overcome the memory constraint of single GPUs. A communicator class which hides the MPI data exchange at the boundaries of the lattice domains, via the low bandwidth PCI-Bus, effectively behind calculations in the inner part of the domain is presented. Linear scaling using 16 NVIDIA Tesla C2070 devices and a maximum performance of 3.5 Teraflops on lattices of size down to 64^3 x 256 is demonstrated.

published version, 40 pages, 8 figures

References in corpus (4)

• Enumerating Gribov copies on the lattice
• Stationary point analysis of the one-dimensional lattice Landau gauge fixing functional, aka random phase XY Hamiltonian
• Landau Gauge Fixing on GPUs
• Hybrid Monte Carlo with Wilson Dirac operator on the Fermi GPU

Cited by in corpus (20)

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• Most Strange Dibaryon from Lattice QCD
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• Dibaryon with highest charm number near unitarity from lattice QCD
• Mirage in Temporal Correlation functions for Baryon-Baryon Interactions in Lattice QCD
• Systematics of the HAL QCD Potential at Low Energies in Lattice QCD
• Consistency between Lüscher's finite volume method and HAL QCD method for two-baryon systems in lattice QCD
• Lattice Calculation of the Decay of Primordial Higgs Condensate
• Coulomb vs. physical string tension on the lattice
• Finite temperature gluon spectral functions from $N_f=2+1+1$ lattice QCD
• Spontaneous Breaking of the BRST Symmetry in the ABJM theory
• Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions
• Potential Energy Landscapes for the 2D XY Model: Minima, Transition States and Pathways
• Overlap Quark Propagator in Coulomb Gauge QCD and the Interrelation of Confinement and Chiral Symmetry Breaking
• Gribov horizon and Gribov copies effect in lattice Coulomb gauge
• Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sector
• Lattice QCD studies on baryon interactions from Lüscher's finite volume method and HAL QCD method
• Spontaneous breaking of nilpotent symmetry in boundary BLG theory
• More effects of Dirac low-mode removal