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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (2): 226-238.doi: 10.3969/j.issn.1005-3085.2015.02.007

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各向异性外问题的非均匀网格的自然边界元法及其耦合法

郑   权,   秦   凤,   高   玥   

  1. 北方工业大学理学院，北京  100144
  • 收稿日期:2013-11-14 接受日期:2014-06-23 出版日期:2015-04-15 发布日期:2015-06-15
  • 基金资助:
    国家自然科学基金 (11471019)；北京市自然科学基金 (1122014).

Natural BEM with Non-uniform Grids and its Coupling Method for Exterior Anisotropic Problems

ZHENG Quan,   QIN Feng,   GAO Yue   

  1. College of Sciences, North China University of Technology, Beijing 100144
  • Received:2013-11-14 Accepted:2014-06-23 Online:2015-04-15 Published:2015-06-15
  • Supported by:
    The National Natural Science Foundation of China (11471019); the Natural Science Foundation of Beijing Municipality (1122014).

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摘要： 本文对于无界区域上各向异性外问题提出了在椭圆边界非均匀网格上的自然边界元法及其与有限元法的耦合法，证明相应的收敛定理和误差估计式，并且在这两种方法中引入基于等分布原理的移动网格技巧．最后，通过数值结果表明了误差收敛理论的正确性以及所提方法和技巧的有效性．

关键词: 各向异性外问题, 椭圆边界, 自然边界元法, 耦合法, 非均匀/移动网格

Abstract:

For the anisotropic problems in 2-D unbounded domains, this paper proposes a natural BEM with non-uniform grids on the elliptic boundary and a coupling of NBEM and FEM with non-uniform grids on the elliptic artificial boundary. Then, the convergence theorems of the NBEM and the coupling method are proved. In addition, the moving mesh method based on equidistribution principle is introduced into the NBEM and the coupling method, respectively. Numerical examples verify the convergence theorems and demonstrate the advantage in accuracy and efficiency of the proposed methods.

Key words: exterior Poisson problem, elliptic boundary, natural BEM, coupling method, non-uniform/moving meshes

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