You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Graphics Processing Units (GPUs) are having a transformational effect on numerical lattice quantum chromo- dynamics (LQCD) calculations of importance in nuclear and particle physics. The QUDA library provides a package of mixed precision sparse matrix linear solvers for LQCD applications, supporting single GPUs based on NVIDIA's Compute Unified Device Architecture (CUDA). This library, interfaced to the QDP++ Chroma framework for LQCD calculations, is currently in production use on the "9g" cluster at the Jefferson Laboratory, enabling unprecedented price performance for a range of problems in LQCD. Nevertheless, memory constraints on current GPU devices limit the problem sizes that can be tackled. In this contribution we describe the parallelization of the QUDA library onto multiple GPUs using MPI, including strategies for the overlapping of communication and computation. We report on both weak and strong scaling for up to 32 GPUs interconnected by InfiniBand, on which we sustain in excess of 4 Tflops.

Cited Abstract(s):
[1]: Abstract 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 chromodynamics (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 NVIDIA's CUDA platform we have implemented a Wilson–Dirac sparse matrix–vector product that performs at up to 40, 135 and 212 Gflops for double, single and half precision respectively on NVIDIA's 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.

[2]: Simulation time for the classical problem of Lattice Quantum Chromodynamics (Lattice QCD) is dominated by one kernel routine responsible for computing the actions of a Dirac operator. This paper describes an experience in parallelizing this kernel routine. We explore parallelization granularities for this kernel routine on Graphical Processing Units (GPUs). We show that fine-grained parallelism can outperform coarse-grained parallelization, given that control-flow and communication effects are minimized. We propose two techniques for transforming control-flow-based code to control-free code. We also show how to reduce the communication effect by optimizing for commonly used sequences of calls to this routine. In our implementation on NVIDIA 8800 GTX, we were able to achieve an 8.3x speedup over an SSE2 optimized version on 2.8 GHz Intel Xeon CPU.

[3]: Abstract The speed, bandwidth and cost characteristics of today's PC graphics cards make them an attractive target as general purpose computational platforms. High performance can be achieved also for lattice simulations but the actual implementation can be cumbersome. This paper outlines the architecture and programming model of modern graphics cards for the lattice practitioner with the goal of exploiting these chips for Monte Carlo simulations. Sample code is also given.

[4]: A method of using veratridine to inhibit nerve impulses, and a composition of matter including veratridine and epinephrine, is provided. Application of veratridine proximal to a nerve causes depolarization of the nerve membrane, thereby blocking transmission of nerve impules. C-fiber selectivity is demonstrated in vitro in rabbit vagus nerves. Veratridine displays extended anesthetic activity over long periods of time when compared to similar local anesthetics, with no local toxicity. Systemic toxicity is reduced by co-injection with epinephrine.

[5]:
GPUs were first used to perform LQCD calculations in [3] . This pioneering study predated various programmability improvements, such as the C for CUDA framework, and hence was implemented using the OpenGL graphics API. It targeted single GPU devices. The QUDA library [5] was discussed extensively in [1] [4] , where the primary techniques and algorithms for maximizing the efficient use of memory bandwidth were presented for a single GPU device. LQCD on GPUs has also been explored in [2] , which focused on questions of fine grained vs. coarse grained parallelism on single GPU devices. In addition, there are several as yet unpublished efforts aimed at exploiting GPUs for LQCD underway.