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边界元近奇异积分计算的迭代Sinh-Sigmoidal组合式变换法

刘静 姚齐水 杨文 周枫林 余江鸿

刘静, 姚齐水, 杨文, 周枫林, 余江鸿. 边界元近奇异积分计算的迭代Sinh-Sigmoidal组合式变换法[J]. 应用数学和力学, 2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167
引用本文: 刘静, 姚齐水, 杨文, 周枫林, 余江鸿. 边界元近奇异积分计算的迭代Sinh-Sigmoidal组合式变换法[J]. 应用数学和力学, 2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167
LIU Jing, YAO Qishui, YANG Wen, ZHOU Fenglin, YU Jianghong. An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements[J]. Applied Mathematics and Mechanics, 2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167
Citation: LIU Jing, YAO Qishui, YANG Wen, ZHOU Fenglin, YU Jianghong. An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements[J]. Applied Mathematics and Mechanics, 2021, 42(4): 385-393. doi: 10.21656/1000-0887.410167

边界元近奇异积分计算的迭代Sinh-Sigmoidal组合式变换法

doi: 10.21656/1000-0887.410167
基金项目: 国家自然科学基金(11602082);湖南省自然科学基金(2018JJ4059);湖南省教育厅科研项目(17B178;19C0577)
详细信息
    作者简介:

    刘静(1995—),女,硕士生(E-mail: 2993318820@qq.com);余江鸿(1978—),男,副教授,博士生,硕士生导师(通讯作者. E-mail: hutyjh@hut.edu.cn).

  • 中图分类号: O343.2

An Iterated Sinh-Sigmoidal Combined Transformation Method for Calculating Nearly Singular Integrals of Boundary Elements

Funds: The National Natural Science Foundation of China(11602082)
  • 摘要: 精确有效地消除积分的近奇异性是三维边界元法在工程应用中的首要问题.当源点与三角形积分单元间的距离无限趋近于零时,会出现近奇异积分问题,积分单元的形状和投影点的位置都是影响近奇异积分计算精度的重要因素.现有的非线性变换法大多只关注径向上积分的近奇异性,而忽略了角度方向和积分单元形状的影响,在投影点接近三角形积分单元边界的情况下,无法获得令人满意的计算精度,并且对子三角形积分单元的形状非常敏感.因此提出了一种改进的基于自适应分块技术和不同坐标变换的迭代sinhsigmoidal组合式变换法,分别消除径向和角度方向积分的近奇异性,在确保计算精度的同时,大大减小了计算规模.数值算例验证了该方法的有效性.
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出版历程
  • 收稿日期:  2020-06-10
  • 修回日期:  2020-07-17
  • 刊出日期:  2021-04-01

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