针对开源有限元软件Calculix传统计算模式在大规模数值计算中的低效问题,提出了Calculix三级并行优化策略,即预处理并行优化、节点间并行调度以及节点内多核多线程并行改造.预处理并行优化在方程组分解过程中与分解过程后,分别对其参数矩阵进行有条件的动态舍弃,据此构造了部分列选主元多行双门槛不完全LU分解预处理算法,并对算法的可行性、有效性以及收敛性给出了证明.为充分发挥TH-2超级计算机强大的资源优势,相继给出了基于QoS的节点间任务动态调度算法,以及节点内多核多线程并行任务调度算法,进一步实现计算任务与资源之间的优化匹配和QoS需求.在实验环节中搭建了针对天河二号(TH-2)超级计算环境的有限元并行计算与分析平台,并完成了针对船舶疲劳强度分析问题的实际工程应用测试.理论分析与工程算例测试结果充分证明:Calculix三级并行优化方案能够有效提高Calculix求解线性方程组的速度,在可获取足够计算资源的前提下,与传统计算模式相比,实际工程算例的计算速度平均提高了2～4倍.%To increase the computing efficiency of Calculix in large scale numerical calculation,this paper researched Calculix and proposed a three-level parallel optimization scheme including preprocessing-level,task level and thread level.A multiple row double threshold incomplete LU matrix decomposition strategy based on column pivoting and dynamic abandon was presented.The corresponding algorithm was given and proved to be efficient,available and convergent.Furthermore,to utilize the powerful computing resources of TH-2 s upercomputer,a task level parallel scheduling algorithm using between computing nodes and a thread level parallel algorithm using between multiple computing cores were also developed and deployed in the experimental platform which focused on the ship fatigue analysis.Both the theory analysis and the actual engineering cases testing were provided to show that the three level parallel optimization scheme based on Calculix can increase the solving speed of liner equations and the analysis efficiency in engineering design areas,and the average speed-up ratio can reach about 2～4 when enough resources can be obtained.
展开▼
