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| Evaluation of nearly singular integrals in boundary element analysis of 3D heat conduction problem with variable coefficients |
| Received:October 03, 2013 Revised:December 28, 2013 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201501002 |
| KeyWord:BEM Nearly singular integral Heat conduction exponential transform Newton-Raphson iteration |
| Author | Institution |
| 赵金军 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 彭海峰 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 原志超 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
| 张耀明 |
山东理工大学 理学院应用数学所, 淄博 |
| 高效伟 |
大连理工大学 工业装备结构分析国家重点实验室, 大连 |
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| Abstract: |
| When the source point is very close to the integrated element in the numerical evaluation of boundary integrals,nearly singularity will appear in the boundary integrals,which results in that the integral can't be calculated directly by using the Gaussian quadrature formulas.A new method for evaluating the nearly singular boundary integral is presented in the paper based on 3D non-homogeneous heat conduction problems.In the proposed method,the Newton-Raphson iteration algorithm is adopted to determine the point on the boundary element which is closest to the source point;and then the distance from the source point to any point on the element is calculated by expanding the coordinates at the point as Taylor series of the closet point;finally,the integration formula for evaluation of the nearly singular boundary integral is derived by substituting the distance function into the nearly singular boundary integral and using the exponential transform method.Two numerical examples for 3D non-homogeneous heat conduction problems are given to verify the correctness,effectiveness and stability of the presented method. |