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共性数学库PETSc(Portable,Extensible Toolkit for Scientific Computation)是高性能计算的基础模块,是超级计算机计算环境的基础算法库之一,其性能直接影响调用数学库的高性能数值计算应用的效率.面向国际上首台100P神威·太湖之光异构超级计算机,根据实际研究需要选取PETSc中两个典型用例ex5(单节点线性求解方程组问题)和ex19(多节点求解2D驱动腔问题)进行实验探究.对运行结果分析找到的热点函数主要为PETSc函数库中7个核心函数,针对这7个核心函数(主要包括向量运算与矩阵运算),提出和实现了其异构并行算法,并结合机器的异构体系结构提出了相应的性能优化方法.在超级计算机上的实验结果为:核心函数并行算法在4主核、256从核的单节点上加速比最大可达到16.4;多节点情况下,当输入规模为16 384时,8192个节点相对于256节点的加速比为32,且加速比随着异构处理器数目的增加接近线性增加,表明PETSc核心函数并行算法在神威·太湖之光超级计算机上具有良好的可扩展性.
The common mathematical library PETSc (Portable, Extensible Toolkit for Scientific Computation) is one of the basic algorithms of supercomputer computing environment, and its performance directly affects the efficiency of high performance numerical computations applied to math library. In the world, the first 100P Shenwei · Taihu Light isomerized supercomputer, two typical cases ex5 (one-node linear equations for solving equations) and ex19 (two-dimensional multi-nodes for solving two-dimensional driving cavity problems) were selected for experiments according to the actual needs of PETSc The hot-spot function found from the operation result analysis is mainly seven core functions in the PETSc library. For these seven core functions (including vector operation and matrix operation), the isomerization parallel algorithm is proposed and implemented, Heterogeneous architecture proposed corresponding performance optimization method.Experimental results on the supercomputer are as follows: The core function parallel algorithm can achieve a maximum speedup ratio of 16.4 on a single 4-core and a 256-node single node, and in multi-node case, When the input size is 16 384, the speedup ratio of 8192 nodes to 256 nodes is 32, and the speedup ratio increases with the number of heterogeneous processors Plus a nearly linear, parallel algorithms show PETSc kernel function has good scalability prowess Taihu light on supercomputers.