| 谢贵重,董云桥,钟玉东,周枫林.基于坐标变换精确计算近奇异积分的双向sinh变换法[J].计算力学学报,2021,38(2):188~192 |
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| 基于坐标变换精确计算近奇异积分的双向sinh变换法 |
| A coordinate transformation based double sinh transformations for evaluation of nearly singular integrals |
| 投稿时间：2020-05-22 修订日期：2020-08-28 |
| DOI：10.7511/jslx20200522002 |
| 中文关键词: 边界元法 边界积分方程 近奇异积分 sinh变换 坐标变换 |
| 英文关键词:boundary element method boundary integral equation nearly singular integrals sinh transformation coordinate transformation |
| 基金项目:国家自然科学基金（11602229；11902141）；中国博士后基金（2019M652753）资助项目. |
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| 中文摘要: |
| 提出一种与坐标变换相结合的双向sinh变换方法用于精确计算近奇异积分。首先利用坐标变换法对近奇异积分进行双向分离，再针对分离出的两个方向的积分形式，根据复变函数极点理论，构造双向sinh变换。与传统结合环向变换和极坐标变换的单向sinh变换以及迭代sinh变换方法相比，双向sinh变换法的计算精度更高，并且最近点的位置对近奇异积分计算精度的影响明显变小。 |
| 英文摘要: |
| This paper presents a new method which combines the coordinate transformation and double sinh transformations for nearly singular integrals.Firstly,the coordinate transformation is employed to separate the near singularities in the two directions.From the forms of the nearly singular integrals in the two directions,based on the complex poles theory,dual sinh transformations are constructed.Compared with the original sinh transformation in polar transformation in combination with the circumference transformation,dual sinh transformation in combination with the coordinate transformation,proposed in our paper can achieve a much more accurate result;moreover,the computational accuracy is less sensitive to position of the nearest singular point in the elements. |
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