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用于解析函数复分析的共轭边界元法

李国清

李国清. 用于解析函数复分析的共轭边界元法[J]. 应用数学和力学, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315
引用本文: 李国清. 用于解析函数复分析的共轭边界元法[J]. 应用数学和力学, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315
LI Guo-qing. A Conjugate Boundary Element Method for Complex Analysis of Analytic Function[J]. Applied Mathematics and Mechanics, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315
Citation: LI Guo-qing. A Conjugate Boundary Element Method for Complex Analysis of Analytic Function[J]. Applied Mathematics and Mechanics, 2017, 38(8): 863-876. doi: 10.21656/1000-0887.370315

用于解析函数复分析的共轭边界元法

doi: 10.21656/1000-0887.370315
基金项目: 国家自然科学基金(10972083)
详细信息
    作者简介:

    李国清(1964—),男,教授,博士(E-mail: lig57@hust.edu.cn).

  • 中图分类号: O174.5;O241.8

A Conjugate Boundary Element Method for Complex Analysis of Analytic Function

Funds: The National Natural Science Foundation of China(10972083)
  • 摘要: 由2个共轭的实调和函数构建1个复解析函数,其复分析在应用数学和力学领域具有重要的作用.提出了一个加权残数方程组,证明了该方程组为2个共轭函数的域内控制方程、边界条件和边界上CauchyRiemann(柯西-黎曼)条件的近似解,等效为复解析函数的逼近方程.在离散空间中,由该加权残数方程分别推导出2个位势问题的直接边界积分方程和1个表示Cauchy-Riemann条件的有限差分方程,随后解决了弱奇异线性方程组的求解难题,并提出用Cauchy积分公式求内点值的方法,从而建立了一种用于复分析的常单元共轭边界元法.最后,用3个算例证明了所提出方法适用于域内或域外的幂函数、指数函数或对数函数形式的解析函数,而且其误差与2维位势问题是同等量级的.
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出版历程
  • 收稿日期:  2016-10-17
  • 修回日期:  2016-12-08
  • 刊出日期:  2017-08-15

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