格点量子色动力学蒸馏算法中关联函数的计算优化

Calculation and optimization of correlation function in distillation method of lattice quantum chromodynamcis

格点量子色动力学(格点QCD)是一种以量子色动力学为基础,被广泛应用于强相互作用相关计算的理论,作为一种可以给出精确可靠理论结果的研究方法,近年来随着计算机能力的提升,正在发挥着越来越重要的作用.蒸馏算法是格点QCD中计算强子关联函数的一种重要数值方法,可以提高所计算物理量的信噪比.但用它来构造关联函数时,同样面临着数据量大和数据维数多的问题,需要进一步提升计算效率.本文开发了一套利用蒸馏算法产生夸克双线性算符的关联函数的程序,利用MPI(message passing interface,消息传递接口,https://www.open-mpi.org),OpenMP(open multi-processing,共享存储并行)和SIMD(single instruction multiple data,单指令多数据流)多级别优化技术解决其中计算性能瓶颈问题.对程序进行了多方面的测试,结果表明本文的设计方案能够支持大规模的计算,在强扩展性测试下512个进程并行计算仍能达到70%左右的效率,大大提升了计算关联函数的能力.

Lattice quantum chromodynamics(lattice QCD)is a theory based on quantum chromodynamics,which is widely used in strong interaction related calculations.As a research method that can give accurate and reliable theoretical results,with the improvement of computer ability,Lattice QCD is playing an increasingly important role in recent years.Distillation method is an important numerical method to calculate hadron correlation function in lattice QCD,and can improve the signal-to-noise ratio of calculated physical quantities.Distillation is a method to approximately compute full propagator via replace the laplacian operator with it’s outerproduct of laplace eigenvectors.In this way,the construction of operators is independent of the inversion of propagator which is costful.The eigenvector system and perambulator can be used in different physical projects and we don’t need to compute these data repeatedly.It’s also convinent for computing disconnected part of correlation function.However,it also faces to the problem of large amount of data in constructing correlation function because the difficulty of compuation is proportional to the cubic of the number of eigenvectors,so it is necessary to further improve its computational efficiency.A program is developed in this work to construct correlation function of quark bilinear with distillation method,and solved the bottleneck of computing performance by using MPI(Message Passing Interface,https://www.open-mpi.org),OpenMP(Open Multi-Processing)and SIMD(Single Instruction Multiple Data)multi-level optimization technology.And this program distribute timeslices to different MPI processes because the computation of each timeslice is independent.In order to show the efficiency of our program some tests result are presented.After various tests of the program,it shows that our design can support large-scale computation.Under the strong scalability test,the parallel computing efficiency of 512 processes can still achieve about 70%.The ability of calculating correlation function is greatly improved.The correction of results also has been checked via compute pseudo-scalar correlators of charmonium.Three different 0-+compared with the effective mass obtained from the tradional method with point source.The results of distillation method are consistent with traditional method.After variational analysis,three state is obtained,which means the variational analysis take effects and the correlation functions obtained from distillation method is reasonable.