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面向磁流体动力学方程组的异构众核全隐求解器研究 被引量:1

RESEARCH ON HETEROGENEOUS MANY-CORE FULLY-IMPLICIT SOLVER FOR MHD DYNAMICAL EQUATIONS
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摘要 磁流体动力学方程组被广泛应用于受控核聚变装置托卡马克、天体物理、磁流体发电等问题的研究中,其往往具有非线性、多尺度、多物理等特征,大规模数值难度较大.目前国际上对不可压缩流体问题的大规模数值求解主要采用全隐或半隐方法,但都是在同构的超级计算机而不是目前主流的异构众核系统上进行计算.论文面向国产神威"太湖之光"超级计算机,开展面向磁流体动力学方程组的异构众核全隐求解器研究.针对Newton-Krylov这类全隐求解器,提出了面向申威26010众核处理器的异构众核并行算法,并对其核心函数开展了众核并行和优化.对核心函数稀疏矩阵向量乘采用Matrix Free的方法来提升性能,对稀疏三角求解采用基于几何信息的异构众核并行算法,针对其访存密集的特点提出了存储格式、数据读取与计算依赖分离、核间寄存器通信等多种优化方法,对非线性残差计算等stencil类计算及10多个向量函数进行了异构众核并行,该异构众核并行算法可被其它应用软件重用.论文采用二维磁场重联问题进行测试,实验结果表明16进程时加速比可达13.6倍,能够支持高分辨率长时间模拟,并准确捕捉磁场重联现象.另外整体并行扩展性已经达到53万核,强可扩展性并行效率达到了33.8%,弱可扩展性并行效率达到了80.7%. The system of magnetohydrodynamics(MHD) equations is usually nonlinear, multiscale and multi-physics, and therefore hard to solve numerically. It is often considered to use fully implicit or semi-implicit method for Incompressible MHD problems, but most efforts have been done on homogeneous supercomputers instead of modern heterogeneous ones. This paper mainly aims at the Chinese homegrown heterogeneous supercomputer,Sunway TaihuLight, and carries out the research on optimizing the fully implicit solver for MHD dynamical equations. This paper proposes both heterogeous parallel algorithms and optimization methods for the kernel functions such as SpMV and SpTRSV in the fully implicit solvers, and develops some optimization technologies for many other kernels for the stencil and vector computations, such as Matrix Free, dynamic-static buffer, register communication. Numerical experiment shows that the speedup can reach about 13.6 times using 16 process, which enables high-resolution long-time simulations for accurately capturing the phenomenon of 2 D magnetic reconnection. In addition, we are able to scale the fully implicit solver to more than 532,480 cores, with a strong scalability of 33.8%, and a weak scalability of 80.7%.
作者 刘芳芳 陈道琨 杨超 赵玉文 Liu Fangfang;Chen Daokun;Yang Chao;Zhao Yuwen(Institute of Software,Chinese Academy of Sciences,Beijing 100190,China;University of Chinese Academy of Sciences,Beijing 100049,China;Peking University,Beijing 100871,China)
出处 《数值计算与计算机应用》 2019年第1期34-50,共17页 Journal on Numerical Methods and Computer Applications
基金 国家重点研发计划高性能计算重点专项(2016YFB0200603) 国家自然科学基金(91530323)资助
关键词 二维磁场重联 磁流体动力学 异构众核 全隐求解器 神威太湖之光 申威26010处理器 2D Magnetic reconnection Magnetohydrodynamics heterogeous manycore computing Sunway TaihuLight SW 26010
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