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Register a new userSolving Lattice QCD systems of equations using mixed precision solvers on GPUs
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Modern graphics hardware is designed for highly parallel numerical tasks and promises significant cost and performance benefits for many scientific applications. One such application is lattice quantum chromodyamics (lattice QCD), where the main computational challenge is to efficiently solve the discretized Dirac equation in the presence of an SU(3) gauge field. Using NVIDIAs CUDA platform we have implemented a Wilson-Dirac sparse matrix-vector product that performs at up to 40 Gflops, 135 Gflops and 212 Gflops for double, single and half precision respectively on NVIDIAs GeForce GTX 280 GPU. We have developed a new mixed precision approach for Krylov solvers using reliable updates which allows for full double precision accuracy while using only single or half precision arithmetic for the bulk of the computation. The resulting BiCGstab and CG solvers run in excess of 100 Gflops and, in terms of iterations until convergence, perform better than the usual defect-correction approach for mixed precision.
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Computing platforms equipped with accelerators like GPUs have proven to provide great computational power. However, exploiting such platforms for existing scientific applications is not a trivial task. Current GPU programming frameworks such as CUDA C/C++ require low-level programming from the developer in order to achieve high performance code. As a result porting of applications to GPUs is typically limited to time-dominant algorithms and routines, leaving the remainder not accelerated which can open a serious Amdahls law issue. The lattice QCD application Chroma allows to explore a different porting strategy. The layered structure of the software architecture logically separates the data-parallel from the application layer. The QCD Data-Parallel software layer provides data types and expressions with stencil-like operations suitable for lattice field theory and Chroma implements algorithms in terms of this high-level interface. Thus by porting the low-level layer one can effectively move the whole application in one swing to a different platform. The QDP-JIT/PTX library, the reimplementation of the low-level layer, provides a framework for lattice QCD calculations for the CUDA architecture. The complete software interface is supported and thus applications can be run unaltered on GPU-based parallel computers. This reimplementation was possible due to the availability of a JIT compiler (part of the NVIDIA Linux kernel driver) which translates an assembly-like language (PTX) to GPU code. The expression template technique is used to build PTX code generators and a software cache manages the GPU memory. This reimplementation allows us to deploy an efficient implementation of the full gauge-generation program with dynamical fermions on large-scale GPU-based machines such as Titan and Blue Waters which accelerates the algorithm by more than an order of magnitude.
Over the past five years, graphics processing units (GPUs) have had a transformational effect on numerical lattice quantum chromodynamics (LQCD) calculations in nuclear and particle physics. While GPUs have been applied with great success to the post-Monte Carlo analysis phase which accounts for a substantial fraction of the workload in a typical LQCD calculation, the initial Monte Carlo gauge field generation phase requires capability-level supercomputing, corresponding to O(100) GPUs or more. Such strong scaling has not been previously achieved. In this contribution, we demonstrate that using a multi-dimensional parallelization strategy and a domain-decomposed preconditioner allows us to scale into this regime. We present results for two popular discretizations of the Dirac operator, Wilson-clover and improved staggered, employing up to 256 GPUs on the Edge cluster at Lawrence Livermore National Laboratory.
We accelerate many-flavor lattice QCD simulations using multiple GPUs. Multiple pseudo-fermion fields are introduced additively and independently for each flavor in the many-flavor HMC algorithm. Using the independence of each pseudo-fermion field and the blocking technique for the quark solver, we can assign the solver task to each GPU card. In this report we present the blocking technique for the many-flavor dynamical QCD simulations. We investigate the effect of the blocking and the acceleration with the multiple GPUs for the Schr{o}dinger functional simulations with Wilson SU(3) plaquette gauge action and $N_f=10$ Wilson fermions. Five pseudo-fermion fields are introduced and the quark solver task is distributed in the ratio of 2:3 to two GPUs. We expect a 40% timing reduction from the single GPU case and have observed a 34% timing reduction in the test simulations.
We search for possibly existent bound states in the heavy-light tetraquark channels with quark content $ bar{b}bar{b}ud $, $ bar{b}bar{b}us $ and $ bar{b}bar{c}ud $ using lattice QCD. We carry out calculations on several gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrices, we also perform a Luscher analysis to extrapolate our results to infinite volume.
We argue that high-precision lattice QCD is now possible, for the first time, because of a new improved staggered quark discretization. We compare a wide variety of nonperturbative calculations in QCD with experiment, and find agreement to within statistical and systematic errors of 3% or less. We also present a new determination of alpha_msbar(Mz); we obtain 0.121(3). We discuss the implications of this breakthrough for phenomenology and, in particular, for heavy-quark physics.
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