基于國產(chǎn)眾核超級計算機(jī)的6×10<sup>5</sup>核并行矩量法

顧宗靜; 吳昊翔; 趙勛旺; 林中朝; 張玉; 張崎

doi:10.11999/JEIT180562

基于國產(chǎn)眾核超級計算機(jī)的6×10⁵核并行矩量法

doi: 10.11999/JEIT180562 cstr: 32379.14.JEIT180562

西安電子科技大學(xué)陜西省超大規(guī)模電磁計算重點(diǎn)實(shí)驗室 ??西安 ??710071

基金項目: 國家重點(diǎn)研發(fā)計劃(2017YFB0202102, 2016YFE0121600)，中國博士后科學(xué)基金(2017M613068)

詳細(xì)信息

作者簡介:
顧宗靜：男，1989年生，博士生，研究方向為計算電磁學(xué)、大規(guī)模并行矩量法、區(qū)域分解算法

吳昊翔：男，1995年生，碩士生，研究方向為計算電磁學(xué)、大規(guī)模并行矩量法

趙勛旺：男，1983年生，副教授，研究方向為大型機(jī)載天線陣列分析

林中朝：男，1988年生，講師，研究方向為計算電磁學(xué)

張玉：男，1978年生，教授，研究方向為計算電磁學(xué)、大規(guī)模并行算法

通訊作者:
趙勛旺　xwzhao@mail.xidian.edu.cn

中圖分類號: TN820
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- 文章訪問數(shù): 2104
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- PDF下載量: 70
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-06-04
- 修回日期: 2018-12-13
- 網(wǎng)絡(luò)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:
為實(shí)現(xiàn)電磁計算的安全可靠和自主可控，該文基于“天河二號”國產(chǎn)眾核超級計算機(jī)平臺，開展大規(guī)模并行矩量法(MoM)的開發(fā)工作。為減輕大規(guī)模并行計算時計算機(jī)集群的通信壓力以及加速矩量法積分方程求解，通過分析矩量法電場積分方程離散生成的矩陣具有對角占優(yōu)特性，提出一種新型LU分解算法，即對角塊矩陣選主元LU分解(BDPLU)算法，該算法減少了panel列分解的計算量，更重要的是，完全消除了選主元過程的MPI通信開銷。利用BDPLU算法，并行矩量法突破了6×10⁵ CPU核并行規(guī)模，這是目前在國產(chǎn)超級計算平臺上實(shí)現(xiàn)的最大規(guī)模的并行矩量法計算，其矩陣求解并行效率可達(dá)51.95%。數(shù)值結(jié)果表明，并行矩量法可準(zhǔn)確高效地在國產(chǎn)超級計算平臺上解決大規(guī)模電磁問題。
- 矩量法 /
- LU分解 /
- 國產(chǎn)超級計算機(jī) /
- 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

圖 1 LU分解過程矩陣特性分布

下載: 全尺寸圖片幻燈片

圖 2 BDPLU算法原理圖

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圖 3 飛機(jī)I仿真模型和雙站RCS結(jié)果

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圖 4 飛機(jī)II雙站RCS結(jié)果

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圖 5 加速比和并行效率

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表 1 CALU算法與BDPLU算法矩陣求解時間對比

FT2000+核數(shù)	矩陣求解時間(s)		并行效率(%)
FT2000+核數(shù)	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

下載: 導(dǎo)出CSV

表 2 BDPLU算法求解矩陣的加速比和并行效率

FT2000+核數(shù)	矩陣求解時間(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

下載: 導(dǎo)出CSV

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