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边界元方法的一些研究进展

刘阳1, 李金2, 胡齐芽3,4, 贾祖朋1, 余德浩3   

  1. 1 IAPCM, 北京应用物理与计算数学研究所, 北京 100094;
    2 华北理工大学理学院, 唐山 063210;
    3 LSEC, 中国科学院数学与系统科学研究院, 计算数学研究所, 北京 100190;
    4 中国科学院大学, 数学科学学院, 北京 100049
  • 收稿日期:2020-03-01 出版日期:2020-08-15 发布日期:2020-08-15
  • 基金资助:

    国家自然科学基金项目(11571352),河北省自然科学基金项目(A2019209533).

刘阳, 李金, 胡齐芽, 贾祖朋, 余德浩. 边界元方法的一些研究进展[J]. 计算数学, 2020, 42(3): 310-348.

Liu Yang, Li Jin, Hu Qiya, Jia Zupeng, Yu Dehao. SOME RESEARCH PROGRESS ON BOUNDARY ELEMENT METHODS[J]. Mathematica Numerica Sinica, 2020, 42(3): 310-348.

SOME RESEARCH PROGRESS ON BOUNDARY ELEMENT METHODS

Liu Yang1, Li Jin2, Hu Qiya3,4, Jia Zupeng1, Yu Dehao3   

  1. 1 IAPCM, Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
    2 College of Science, North China University of Science and Technology, Tangshan 063210, China;
    3 LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China;
    4 School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2020-03-01 Online:2020-08-15 Published:2020-08-15
本文旨在综述我们小组近二十年来在边界元方法这一领域的一些研究成果,在简要介绍边界元方法的基本思想后,主要介绍了一类非线性界面问题的有限元-边界元耦合方法、求解电磁散射问题的有限元-边界元耦合方法和超奇异积分的一类计算方法.
In this paper we try to recall some main progresses of our group on the boundary element methods in the last 20 years. We first outline the basic ideas of the boundary element methods. Then we simply introduce coupling methods between finite element and boundary element for a certain nonlinear interface problem in unbounded domains, coupling methods between finite element and boundary element for electromagnetic scattering problems and some computational methods for hypersingular integrals.

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