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二维Helmholtz方程的插值型边界无单元法

陈林冲 李小林

陈林冲, 李小林. 二维Helmholtz方程的插值型边界无单元法[J]. 应用数学和力学, 2018, 39(4): 470-484. doi: 10.21656/1000-0887.380202
引用本文: 陈林冲, 李小林. 二维Helmholtz方程的插值型边界无单元法[J]. 应用数学和力学, 2018, 39(4): 470-484. doi: 10.21656/1000-0887.380202
CHEN Linchong, LI Xiaolin. An Interpolating Boundary Element-Free Method for 2D Helmholtz Equations[J]. Applied Mathematics and Mechanics, 2018, 39(4): 470-484. doi: 10.21656/1000-0887.380202
Citation: CHEN Linchong, LI Xiaolin. An Interpolating Boundary Element-Free Method for 2D Helmholtz Equations[J]. Applied Mathematics and Mechanics, 2018, 39(4): 470-484. doi: 10.21656/1000-0887.380202

二维Helmholtz方程的插值型边界无单元法

doi: 10.21656/1000-0887.380202
基金项目: 国家自然科学基金(面上项目)(11471063);重庆市基础科学与前沿技术研究重点项目(cstc2015jcyjBX0083)
详细信息
    作者简介:

    陈林冲(1988—),男,硕士(E-mail: 794530653@qq.com);李小林(1983—),男,教授,博士(通讯作者. E-mail: lxlmath@163.com).

  • 中图分类号: O242.2

An Interpolating Boundary Element-Free Method for 2D Helmholtz Equations

Funds: The National Natural Science Foundation of China(General Program)(11471063)
  • 摘要: 针对二维Helmholtz方程的内外边值问题,提出了插值型边界无单元法(interpolating boundary element-free method).在间接位势理论的基础上,利用Laplace方程基本解的特性,建立了求解Helmholtz方程Neumann边值内外问题的正则化形式,有效消除了强奇异积分的计算.其次通过引入全局距离展开成局部距离的幂级数, 详细推导了距离函数的导数和法向导数差值的极限表达式.最后给出了4个插值型边界无单元法的数值算例, 表明了该方法可取得较高的可行性和有效性.
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出版历程
  • 收稿日期:  2017-07-20
  • 修回日期:  2017-11-27
  • 刊出日期:  2018-04-15

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