Domain decomposition method on GPU cluster for Lattice

Abstract

Pallalel GPGPU computing for lattice QCD simulations has a bottleneck on the GPU to GPU data communication due to the lack of the direct data exchanging facility. In this work we investigate the performance of quark solver using the restricted additive Schwarz (RAS) preconditioner on a low cost GPU cluster. We expect that the RAS preconditioner with appropriate domaindecomposition and task distribution reduces the communication bottleneck. The GPU cluster we constructed is composed of four PC boxes, two GPU cards are attached to each box, and we have eight GPU cards in total. The compute nodes are connected with rather slow but low cost Gigabit-Ethernet. We include the RAS preconditioner in the single-precision part of the mixedprecision nested-BiCGStab algorithm and the single-precision task is distributed to the multiple GPUs. The benchmarking is done with the O(a)-improved Wilson quark on a randomly generated gauge configuration with the size of 32 4 . We observe a factor two improvment on the solver performance with the RAS precoditioner compared to that without the preconditioner and find that the improvment mainly comes from the reduction of the communication bottleneck as we expected.

ΛΛ and NΞ interactions from lattice QCD near the physical point

“…The latter allows us to average over the forward propagation and backward propagation in time due to time-reversal and charge conjugation symmetries. The quark propagators from the wall source with the Coulomb gauge fixing are calculated by the domain-decomposed solver [22,23,24,25], and then the efficient algorithm developed in [26] is employed to calculate correlation functions.…”

NΩ dibaryon from lattice QCD near the physical point

“…The periodic (Dirichlet) boundary condition for the spatial (temporal) direction is imposed for quarks. The quark propagators are obtained by using the domaindecomposed solver [32,33,34,35], and the unified contraction algorithm is employed to calculate the correlation functions [36].…”

Most Strange Dibaryon from Lattice QCD

“…We pick 1 configuration per each 5 trajectories, and make use of the rotation symmetry and the translational invariance for the source position to increase the statistics. The total statistics in this Letter amounts to 400 configurations × 2 (forward/backward) [ [34][35][36][37] and the correlation functions are calculated using the unified contraction algorithm [38].…”