基于GPU的混合精度求解器求解格点量子色动力学方程组
Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
摘要：
现代图形硬件专为高度并行的数值任务而设计，并为许多科学应用提供了显着的成本和性能优势。一个这样的应用是格点量子色动力学（格点量子色动力学），其中主要的计算挑战是在SU（3）规范场的存在下有效地求解离散的狄拉克方程。使用NVIDIA的CUDA平台，我们实现了Wilson-Dirac稀疏矩阵向量积，在NVIDIA的GeForce GTX 280 GPU上分别以高达40 Gflops、135 Gflops和212 Gflops的速度执行双精度、单精度和半精度运算。我们已经开发了一种新的混合精度的方法，Krylov求解器使用可靠的更新，允许完全双精度精度的准确性，而只使用单精度或半精度的算法的大部分计算。由此产生的BiCGstab和CG解算器运行速度超过100 Gflops，并且在收敛之前的迭代方面，比通常的缺陷校正方法在混合精度方面表现更好。
英文摘要：
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 NVIDIA's 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 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.
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