矩的显式积分算法研究与应用

付子豪; 龚光红

doi:10.13700/j.bh.1001-5965.2014.0266

矩的显式积分算法研究与应用

doi: 10.13700/j.bh.1001-5965.2014.0266

付子豪,
龚光红^,

北京航空航天大学自动化科学与电气工程学院, 北京 100191

详细信息

作者简介:
付子豪(1990—),男,四川德阳人,硕士生,fuzihaofzh@gmail.com

通讯作者:
龚光红(1968—),女,四川石柱人,教授,ggh@buaa.edu.cn,主要研究方向为分布仿真与虚拟技术.

中图分类号: TP301.6
计量
- 文章访问数: 1184
- HTML全文浏览量: 87
- PDF下载量: 733
- 被引次数: 0
出版历程
- 收稿日期: 2014-05-13
- 修回日期: 2014-08-25
- 网络出版日期: 2015-04-20

Explicit moment integration algorithm and its application

FU Zihao,
GONG Guanghong^,

School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

摘要

摘要: 矩的求解通常被用于求解有限元、体积、惯性矩等问题中.基于矩的叠加性,首先给出了在三维空间中计算域的离散方式,并推导了矩的显式积分公式,随后将其推广到n维空间中,该表达式易于在计算机上实现;设计了矩的并行计算算法,并通过Fortran和Python混编的方式,实现了矩的并行计算;对多重精度下的样例数据给出了一个算例,实现了零阶矩和二阶矩的计算,并和串行算法、逐次降维算法作出比较,进行了效率分析和误差分析.结果显示,矩的显式积分并行计算算法易于程序实现,并且在效率上高于串行算法,能够很容易推广到高维空间,该算法具有高度可并行性,误差主要来自计算域离散.
- 矩 /
- 显式积分公式 /
- 并行计算 /
- 逐次降维 /
- 计算域离散
Abstract: The calculation of moment is often used in finite element method, volume calculation, moment of inertia calculation, etc. A discrete method of the computational domain in three-dimensional space was proposed firstly based on the superposition of moment. An explicit formula was derived in three-dimensional space and then extended to n-dimensional space, which can be easily implemented on the computer. Secondly, a parallel algorithm of moment calculation was designed and implemented with mixed Fortran and Python. Thirdly, a zero-order and second-order moment was calculated in a multi-fidelity example. The efficiency of the algorithm was compared with a serial algorithm and a successive dimensionality reduction algorithm. Meanwhile, efficiency analysis and error analysis were presented. The result shows that the explicit moment integration algorithm can be easily implemented with programs and runs faster than the serial algorithm. It is highly parallel and can also be easily extended to a higher dimensional space. The algorithm is highly parallel, whose error mainly comes from the discrete process of the computational domain.
- moment /
- explicit moment formula /
- parallel computing /
- successive dimensionality reduction /
- discrete computational domain

HTML全文

参考文献(15)

[1]	Johnson F T, Samant S S,Bieterman M B,et al.TRANAIR-a computer code for transonic analyses of arbitrary configurations,NASA-CR-4348[R].Washington,D.C.:NASA,1987.
[2]	洪国雄. 惯性张量的物理意义[J].大学物理,1989,12(1):7-8. Hong G X.The physical meaning of the inertia tensor[J].College Physics,1989,12(1):7-8(in Chinese).
[3]	秦莉,杨明, 郭庆.遗传算法在质量矩导弹姿态控制中的应用[J].北京航空航天大学学报,2007,33(7):769-772. Qin L,Yang M,Guo Q.Movingmass attitude control law based on genetic algerithm[J].Journal of Beijing University of Aeronautics and Astronautics,2007,33(7):769-772(in Chinese).
[4]	徐水源. 惯性矩与惯性张量的关系[J].黄石教育学院学报,2005,22(4):90-92. Xu S Y.The relationship of the moment of inertia and inertia tensor[J].Journal of Huangshi Education College,2005,22(4):90-92(in Chinese).
[5]	Soerjadi R. On the computation of the moments of a polygon,with some applications[M].Netherlands:Stevin Laboratory,1968:43-58.
[6]	Mirtich B. Fast and accurate computation of polyhedral mass properties[J].Journal of Graphics Tools,1996,1(2):31-50.
[7]	Sheynin S, Tuzikov A,Vasiliev P.Efficient computations of body moments[J].Информационные Процессы,2002,2(1):22- 23.
[8]	Sheynin S A, Tuzikov A V.Explicit formulae for polyhedra moments[J].Pattern Recognition Letters,2001,22(10):1103- 1109.
[9]	Tuzikov A V, Sheynin S A,Vasiliev P V.Computation of volume and surface body moments[J].Pattern Recognition,2003,36(11): 2521-2529.
[10]	Hall M. Combinatorial theory[M].New York:John Wiley & Sons,1998:166.
[11]	VanRossum G, Drake F L.Python language reference manual[M].United Kingdom:Network Theory,2003.
[12]	VanRossum G, Drake F L.The python language reference[M].Beaverton,OR,USA:Python Software Foundation,2010.
[13]	Chandra R. Parallel programming in OpenMP[M].San Francisco:Morgan Kaufmann,2001.
[14]	Dagum L, Menon R.OpenMP:an industry standard API for shared-memory programming[J].Computational Science & Engineering,IEEE,1998,5(1):46-55.
[15]	Fredericks W J, Antcliff K R,Costa G,et al.Aircraft conceptual design using vehicle sketch pad[C]//48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition.Reston:American Institute of Aeronautics and Astronautics Inc,2010:1-17.