| 三维Laplace方程边界元中线性单元的精确积分法 |
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| 引用本文： | 袁政强,黄剑,祝家麟. 三维Laplace方程边界元中线性单元的精确积分法[J]. 应用力学学报, 2004, 21(3): 117-120 |
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| 作者姓名： | 袁政强 黄剑 祝家麟 |
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| 作者单位： | 1. 重庆大学土木工程学院,重庆,400045
2. 重庆大学数理学院,重庆,400044 |
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| 摘 要： | 边界元中的边界积分计算影响计算精度和计算速度。非奇异积分一般采用数值积分，当配置点接近积分单元时，计算精度降低。未知函数线性插值得到的解是连续解，但计算难度增大。本文采用积分区域变换，将三维Laplace问题的二维积分化为一维积分，这样奇异积分和非奇异积分能采用精确积分的方法计算，使求解精度，计算速度都得到提高。
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| 关 键 词： | 边界元 Laplace方程 精确积分 |
| 文章编号： | 1000-4939(2004)03-0117-04 |
Exact Integration of the Linear Element of Laplace Equation In Boundary Element Method |
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| Yuan Zhengqiang Huang Jian Zhu Jialin. Exact Integration of the Linear Element of Laplace Equation In Boundary Element Method[J]. Chinese Journal of Applied Mechanics, 2004, 21(3): 117-120 |
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| Authors: | Yuan Zhengqiang Huang Jian Zhu Jialin |
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| Affiliation: | Yuan Zhengqiang~1 Huang Jian~1 Zhu Jialin~2 |
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| Abstract: | The boundary integral in Boundary Element Method affects the precision and the speed of the method. The nonsingular integrals are popularly calculated by the Gauss numerical integral, and they are low in precision when the source points approach the element. The solution by the interpolation of unknown function is continous, which makes the calculation more difficult. This paper presents an alternative way to transform the double integral in Laplace problem on 3-d into the linear integrals on the boundary of each subdomain, so that all the singular integrals and nonsingular integrals are calculated by analytical method. It makes the precision and the speed of BEM improved. |
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| Keywords: | boundary element method laplace equations exact integral. |
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