北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (4): 727-731.doi: 10.13700/j.bh.1001-5965.2014.0266

• 论文 • 上一篇    下一篇

矩的显式积分算法研究与应用

付子豪, 龚光红   

  1. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191
  • 收稿日期:2014-05-13 修回日期:2014-08-25 出版日期:2015-04-20 发布日期:2015-05-08
  • 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. E-mail:ggh@buaa.edu.cn
  • 作者简介:付子豪(1990—),男,四川德阳人,硕士生,fuzihaofzh@gmail.com

Explicit moment integration algorithm and its application

FU Zihao, GONG Guanghong   

  1. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2014-05-13 Revised:2014-08-25 Online:2015-04-20 Published:2015-05-08

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.

关键词: 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.

Key words: moment, explicit moment formula, parallel computing, successive dimensionality reduction, discrete computational domain

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