EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

二维正交各向异性位势问题的高阶单元快速多极边界元法

李聪 胡斌 胡宗军 牛忠荣

李聪, 胡斌, 胡宗军, 牛忠荣. 二维正交各向异性位势问题的高阶单元快速多极边界元法[J]. 力学学报, 2021, 53(4): 1038-1048. doi: 10.6052/0459-1879-20-455
引用本文: 李聪, 胡斌, 胡宗军, 牛忠荣. 二维正交各向异性位势问题的高阶单元快速多极边界元法[J]. 力学学报, 2021, 53(4): 1038-1048. doi: 10.6052/0459-1879-20-455
Li Cong, Hu Bin, Hu Zongjun, Niu Zhongrong. ANALYSIS OF 2-D ORTHOTROPIC POTENTIAL PROBLEMS USING FAST MULTIPOLE BOUNDARY ELEMENT METHOD WITH HIGHER ORDER ELEMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1038-1048. doi: 10.6052/0459-1879-20-455
Citation: Li Cong, Hu Bin, Hu Zongjun, Niu Zhongrong. ANALYSIS OF 2-D ORTHOTROPIC POTENTIAL PROBLEMS USING FAST MULTIPOLE BOUNDARY ELEMENT METHOD WITH HIGHER ORDER ELEMENTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1038-1048. doi: 10.6052/0459-1879-20-455

二维正交各向异性位势问题的高阶单元快速多极边界元法

doi: 10.6052/0459-1879-20-455
基金项目: 1)国家自然科学基金(11272111);博士启动基金(2020QDZ08)
详细信息
    作者简介:

    3)胡斌, 博士, 主要研究方向: 固体力学. E-mail: hubin347@163.com
    2)李聪, 讲师, 主要研究方向: 固体力学. E-mail: Licong@ahjzu.edu.cn;

    通讯作者:

    李聪

    胡斌

  • 中图分类号: O343.2

ANALYSIS OF 2-D ORTHOTROPIC POTENTIAL PROBLEMS USING FAST MULTIPOLE BOUNDARY ELEMENT METHOD WITH HIGHER ORDER ELEMENTS

  • 摘要: 研制了一种适用于二维正交各向异性位势问题的高阶单元(线性单元和二次单元)快速多极边界元法. 在快速多极边界元法中, 源点对于远场区域的积分采用快速多极展开式计算, 而对于近场区域的积分则直接进行计算. 高阶单元的使用使得近场积分, 尤其是奇异积分和几乎奇异积分的计算更加复杂. 通过引入复数表达对其进行简化, 若边界采用线性单元插值, 近场积分可直接解析计算; 若采用二次单元插值, 则给出一个半解析算法计算近场积分. 高阶单元奇异积分和几乎奇异积分计算难题的解决, 使得高阶单元快速多极边界元法不仅能够计算一般结构, 也能被应用于超薄体结构, 拓宽了高阶单元快速多极边界元法的适用范围. 数值算例表明, 若计算精度一定, 高阶单元快速多极边界元法较常值单元快速多极边界元法使用的单元数量显著减少, 且高阶单元快速多极边界元法计算时间与自由度数量成线性关系, 其计算效率仍处于$O(N)$量级, 因此高阶单元快速多极边界元法可更加高效求解大规模问题.

     

  • [1] 杜庆华, 岑章志, 稽醒 等. 边界积分方程方法 —— 边界元法. 北京: 高等教育出版社, 1989

    (Du Qinghua, Qin Zhangzhi, Ji Xing, et al. Boundary Integral Equation-Boundary Element Method. Beijing: High Education Press, 1989 (in Chinese))
    [2] Barnes J, Hut P. A hierarchical O ($Nlog N$) force calculation algorithm. Nature, 1986,324:446-449
    [3] Greengard L, Rokhlin V. A fast algorithm for particles simulations. Journal of Computational Physics, 1987,73:325-348
    [4] Aimi A, Diligenti M, Lunardini F, et al. A new application of panel clustering method for 3D SGBEM. Computer Modeling in Engineering & Sciences, 2003,4(1):31-50
    [5] Helsing J, Jonsson A. Stress calculation on multiply connected domains. Journal of Computational Physics, 2002,176:456-482
    [6] Aoki S, Amaya K, Urago M, et al. Fast multipole boundary element analysis of corrosion problems. Computer Modeling in Engineering & Science, 2004,6(2):123-132
    [7] Wang PB, Yao ZH, Wei Y. FM-BEM evaluation for effective elastic moduli of micro cracked solids. Tsinghua Science and Technology, 2007,12(5):562-566
    [8] Wang PB, Yao ZH. Fast multipole boundary element analysis of two-dimensional elastoplastic problems. Communications in Numerical Methods in Engineering, 2007,23(10):889-903
    [9] Wang WW, Chen YM. Mathematical foundation of the fast multipole BEM for 2D potential problems. Advanced Materials Research, 2010, 143-144:1190-1194
    [10] Pierce AP, Napier JAL. A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics. International Journal for Numerical Methods in Engineering, 1995,38:4009-4034
    [11] Liu YJ, Li YX, Xie W. Modeling of multiple crack propagation in 2-D elastic solids by the fast multiple boundary element method. Engineering Fracture Mechanics, 2017,172:1-16
    [12] 吴清华. 高振荡Henkel核积分方程的高效数值算法. 数学物理学报, 2019,39A(3):611-619

    (Wu Qinghua. Efficient numerical method for integral equations with oscillatory Henkel kernels. Acta Mathematica Scientia, 2019,39A(3):611-619 (in Chinese))
    [13] Zhang JM, Zhuang C, Qin X, et al. FMM accelerated hybrid boundary node method for multi-domain problems. Engineering Analysis with Boundary Elements, 2010,34(5):433-439
    [14] Zhang JM, Tanaka M. Adaptive spatial decomposition in fast multipole method. Journal of Computational Physics, 2007,226(1):17-28
    [15] 刘中宪, 孙帅杰, 赵瑞斌 等. 基于快速多极边界元法的局部场地对地震波高频散射二维模拟. 岩土工程学报, 2017,39(11):2017-2025

    (Liu Zhongxian, Sun Shuaijie, Zhao Ruibin, et al. Two-dimensional simulation of high frequency scattering of seismic waves by local sites based on fast multi-pole boundary element method. Chinese Journal of Geotechnical Engineering, 2017,39(11):2017-2025 (in Chinese))
    [16] 刘中宪, 符瞻远, 苗雨 等. 非连续屏障对Rayleigh波宽频散射三维快速边界元模拟. 振动与冲击, 2019,38(19):89-97

    (Liu Zhongxian, Fu Zhanyuan, Mian Yu, et al. 3-D simulation for broadband scattering of Rayleigh wave by discontinuous barrier based on FMP-IBEM. Journal of Vibration and Shock, 2019,38(19):89-97 (in Chinese))
    [17] Han YC, Nie YF, Dong H. A fast multipole algorithm for radiate heat transfer in 3D semitransparent media. Journal of Quantitative Spectroscopy and Radiate Transfer, 2018,221:8-17
    [18] Qu WZ, Zheng CJ, Zhang YM, et al. A wideband fast multipole accelerated singular boundary method for three-dimensional acoustic problems. Computers and Structures, 2018,206(8):82-89
    [19] Nishimura N, Yoshida KI, Kobayashi S. A fast multipole boundary integral equation method for crack problems in 3D. Engineering Analysis with Boundary Elements, 1999,23(1):97-105
    [20] 赵丽滨, 姚振汉. 快速多极边界元法在薄板结构中的应用. 燕山大学学报, 2004,6(2):103-106

    (Zhao Libin, Yao Zhenhan. Application of fast multipole boundary element method for thin plate structures. Journal of Yanshan University, 2004,6(2):103-106 (in Chinese))
    [21] Wang HT, Yao ZH. A new fast multipole boundary element method for large scale analysis of mechanical properties in 3D particle-reinforced composites. Computer Modeling in Engineering & Sciences, 2005,7(1):85-95
    [22] Zhang JM, Tanaka M, Endo M. The hybrid boundary node method accelerated by fast multipole expansion technique for 3D potential problems. International Journal for Numerical Methods in Engineering, 2005,63(5):660-680
    [23] Hosseinzadeh H, Dehghan M. A simple and accurate scheme based on complex space C to calculate boundary integrals of 2D boundary elements method. Computers and Mathematics with Applications, 2014,68:531-542
    [24] Johnston BM, Johnston PR, Elliott D. A sinh transformation for evaluating two-dimensional nearly singular boundary element integrals. International Journal for Numerical Methods in Engineering, 2007,69(7):1460-1479
    [25] Gu Y, He X, Chen W, et al. Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method. Computers & Mathematics with Applications, 2018,75(1):33-44
    [26] Takayuki M. Fast calculation of far-field sound directivity based on fast multipole boundary element method. Journal of Theoretical and Computational Acoustics, 2020,28(4):1-22
    [27] 牛忠荣, 胡宗军, 葛仁余 等. 二维弹性力学边界元法高阶单元几乎奇异积分半解析算法. 力学学报, 2013,45(6):897-907

    (Niu Zhongrong, Hu Zhongjun, Ge Renyu, et al. A new semi-analytic algorithm of nearly singular integrals in high order boundary element analysis of 2D elasticity. Chinese Journal of Theoretical and Applied Mechanics, 2013,45(6):897-907 (in Chinese))
    [28] 牛忠荣, 王秀喜, 周焕林. 边界元法计算近边界点参量的一个通用算法. 力学学报, 2001,33(2):275-283

    (Niu Zhongrong, Wang Xiuxi, Zhou Huanlin. A general algorithm for calculating the quantities at interior points close to the boundary by the BEM. Chinese Journal of Theoretical and Applied Mechanics, 2001,33(2):275-283 (in Chinese))
    [29] Liu YJ, Nishimura N. The fast multipole boundary element method for potential problems: A tutorial. Engineering Analysis with Boundary Elements, 2006,30(5):371-381
  • 加载中
计量
  • 文章访问数:  259
  • HTML全文浏览量:  36
  • PDF下载量:  79
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-12-29
  • 刊出日期:  2021-04-10

目录

    /

    返回文章
    返回