| 三维位势问题边界元法中几乎奇异积分的正则化 |
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| 引用本文： | 周焕林,牛忠荣,王秀喜.三维位势问题边界元法中几乎奇异积分的正则化[J].计算物理,2005,22(6):501-506. |
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| 作者姓名： | 周焕林 牛忠荣 王秀喜 |
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| 作者单位： | 合肥工业大学,工程力学系,安徽,合肥,230009;中国科学技术大学,中科院材料力学行为和设计重点实验室,安徽,合肥,230026 |
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| 基金项目： | 国家自然科学基金(10272039)资助项目 |
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| 摘 要： | 采用一种半解析正则化算法,计算了三维位势问题边界元法中近边界点的几乎强奇异和几乎超奇异面积分.该算法适用于三角形线性等参元.对高次单元将其细分为几个三节点三角形单元即可应用该算法.由于几乎奇异性,与内点邻近的单元上的积分,采用半解析正则化积分算法计算;而远处单元的积分仍保持常规高斯积分.对三维热传导算例,计算了近边界点的温度和热流.数值结果证明了该算法的有效性和精确性.
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| 关 键 词： | 边界元法 几乎奇异积分 正则化 三维位势问题 热传导 |
| 文章编号： | 1001-246X（2005）06-0501-06 |
| 收稿时间： | 2004-07-29 |
| 修稿时间： | 2005-01-28 |
Regularization of Nearly Singular Integrals in the Boundary Element Method for 3-D Potential Problems |
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| ZHOU Huan-lin,NIU Zhong-rong,WANG Xiu-xi.Regularization of Nearly Singular Integrals in the Boundary Element Method for 3-D Potential Problems[J].Chinese Journal of Computational Physics,2005,22(6):501-506. |
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| Authors: | ZHOU Huan-lin NIU Zhong-rong WANG Xiu-xi |
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| Institution: | 1. Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, China ; 2. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230026, China |
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| Abstract: | A semi-analytical integral regularization algorithm is applied to the evaluation of nearly strongly-singular and nearly hypersingular surface integrals in the boundary element method(BEM) for three-dimensional potential problems.The algorithm is available for linear triangular isoparametric elements.The algorithm can be used to higher order elements by subdividing the element into triangular sub-elements.Due to singularity,the semi-analytical integral regularization algorithm is applied to the integral element close to the source point.The conventional Gauss quadrature is kept in the integral element far away from the inner point.The potentials and fluxes at the interior points close to the boundary are computed for three-dimensional heat conduction examples.The results demonstrate the accuracy and effectiveness of the algorithm. |
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| Keywords: | BEM nearly singular integral regularization 3-D potential problem heat conduction |
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