基于国产众核超级计算机的6×10<sup>5</sup>核并行矩量法

顾宗静; 吴昊翔; 赵勋旺; 林中朝; 张玉; 张崎

doi:10.11999/JEIT180562

基于国产众核超级计算机的6×10⁵核并行矩量法

doi: 10.11999/JEIT180562

西安电子科技大学陕西省超大规模电磁计算重点实验室西安 710071

基金项目: 国家重点研发计划(2017YFB0202102, 2016YFE0121600)，中国博士后科学基金(2017M613068)

详细信息

作者简介:
顾宗静：男，1989年生，博士生，研究方向为计算电磁学、大规模并行矩量法、区域分解算法

吴昊翔：男，1995年生，硕士生，研究方向为计算电磁学、大规模并行矩量法

赵勋旺：男，1983年生，副教授，研究方向为大型机载天线阵列分析

林中朝：男，1988年生，讲师，研究方向为计算电磁学

张玉：男，1978年生，教授，研究方向为计算电磁学、大规模并行算法

通讯作者:
赵勋旺　xwzhao@mail.xidian.edu.cn

中图分类号: TN820
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出版历程
- 收稿日期: 2018-06-04
- 修回日期: 2018-12-13
- 网络出版日期: 2018-12-19
- 刊出日期: 2019-04-01

Parallel MoM Using the Six Hundred Thousand Cores on Domestically-made and Many-core Supercomputer

Shaanxi Key Laboratory of Large Scale Electromagnetic Computing, Xidian University, Xi’an 710077, China

Funds: The National Key Research and Development Program of China (2017YFB0202102, 2016YFE0121600), The China Postdoctoral Science Foundation (2017M613068)

摘要

摘要:
为实现电磁计算的安全可靠和自主可控，该文基于“天河二号”国产众核超级计算机平台，开展大规模并行矩量法(MoM)的开发工作。为减轻大规模并行计算时计算机集群的通信压力以及加速矩量法积分方程求解，通过分析矩量法电场积分方程离散生成的矩阵具有对角占优特性，提出一种新型LU分解算法，即对角块矩阵选主元LU分解(BDPLU)算法，该算法减少了panel列分解的计算量，更重要的是，完全消除了选主元过程的MPI通信开销。利用BDPLU算法，并行矩量法突破了6×10⁵ CPU核并行规模，这是目前在国产超级计算平台上实现的最大规模的并行矩量法计算，其矩阵求解并行效率可达51.95%。数值结果表明，并行矩量法可准确高效地在国产超级计算平台上解决大规模电磁问题。
- 矩量法 /
- LU分解 /
- 国产超级计算机 /
- 6×10⁵核
Abstract:
In order to realize safety, reliability and self-control of electromagnetic computing, the large-scale parallel MoM is studied based on domestically-made many-core supercomputer platform named " Tianhe-2”. A new LU decomposition algorithm named Block Diagonal matrix Pivoting LU decomposition (BDPLU) algorithm, is proposed by analyzing the diagonally dominant characteristics of the matrix generated through dispersing electric field integral equation of MoM, for the purpose of communication pressure reduction to computer cluster and solution acceleration to MoM integral equation during large-scale parallel computation. The BDPLU algorithm reduces the amount of calculation in the process of panel factorization. More importantly, the algorithm completely eliminates MPI communication when pivoting. Using BDPLU algorithm, the maximum number of CPU cores break through 6×10⁵ CPU cores, which is the largest scale of parallel MoM computation in domestically-made and many-core supercomputing platform at present, and the parallel efficiency of solving matrix can reach 51.95%. Numerical results show that parallel MoM can accurately and efficiently solve large-scale electromagnetic field problems on domestic supercomputing platform.
- Method of Moments (MoM) /
- LU decomposition /
- Domestically-made supercomputer /
- 6×10⁵ cores

HTML全文

图 1 LU分解过程矩阵特性分布

下载: 全尺寸图片幻灯片

图 2 BDPLU算法原理图

下载: 全尺寸图片幻灯片

图 3 飞机I仿真模型和双站RCS结果

下载: 全尺寸图片幻灯片

图 4 飞机II双站RCS结果

下载: 全尺寸图片幻灯片

图 5 加速比和并行效率

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表 1 CALU算法与BDPLU算法矩阵求解时间对比

FT2000+核数	矩阵求解时间(s)		并行效率(%)
FT2000+核数	CALU	BDPLU	CALU	BDPLU
2000	796.54	742.57	100	100
3000	567.78	518.68	93.53	95.44
4000	463.93	421.12	85.85	88.17
5000	386.89	338.24	82.35	87.82
10000	226.57	187.83	70.31	79.07
15000	172.91	139.05	61.42	71.20
20000	133.97	118.38	59.46	62.73
40000	72.83	64.61	54.68	57.47

下载: 导出CSV

表 2 BDPLU算法求解矩阵的加速比和并行效率

FT2000+核数	矩阵求解时间(s)	加速比	并行效率(%)
9600	29183.33	1	100
48000	6336.53	4.61	92.11
96000	3501.73	8.33	83.34
192000	2035.35	14.34	71.69
240000	1764.53	16.54	66.16
336000	1328.13	21.97	62.78
384000	1227.91	23.77	59.42
432000	1133.64	25.74	57.21
480000	1043.45	27.97	55.94
504000	997.94	29.24	55.70
552000	937.82	31.12	54.12
600000	898.81	32.49	51.95

下载: 导出CSV

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