| REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS |
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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： | Department of Mechanics，University of Science and Technology of China，Department of Engineering Mechanics，Hefei University of Technology，Department of Mechanics，University of Science and Technology of China Hefei 230026，P.R.China，Hefei 230009，P.R.China，Hefei 230026，P.R.China |
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| 基金项目： | theNationalNaturalScienceFoundationofChina (1 0 2 72 0 3 9) |
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| 摘 要： | IntroductionAsanimportantnumericalmethod ,BoundaryElementMethod (BEM)hasbeenappliedinmanyareas1].However,theBEMhasthedifficultiesofcalculatingsingularintegralsatnodesonboundaryoratinteriorpointsveryclosetotheboundary .TheaccuracyoftheBEMdependsontheprecisionofthecalculatedvaluesofthesingularintegrals,toagreatdegree.Manyresearchersdevotethemselvestothetreatmentofthesingularintegrals2～3],whicharereviewedindetailbyRef.4] .Ageneralregularizationalgorithmofevaluatingthephysicalquantitiesa…
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| 收稿时间： | 27 November 2001 |
Regularization of nearly singular integrals in the boundary element method of potential problems |
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| Huan-lin,Zhou,Zhong-rong,Niu,Xiu-xi,Wang.REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS[J].Applied Mathematics and Mechanics(English Edition),2003,24(10):1208-1214. |
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| Authors: | Huan-lin Zhou Zhong-rong Niu Xiu-xi Wang |
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| Institution: | 1. Department of Mechanics, University of Science and Technology of China, Hefei 230026, P.R. China
2. Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, P.R. China |
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| Abstract: | A general algorithm is applied to the regularization of nearly singular integrals in the boundary element method of planar potential problems. For linear elements, the strongly singular and hypersingular integrals of the interior points very close to boundary were categorized into two forms. The factor leading to the singularity was transformed out of the integral representations with integration by parts, so non-singular regularized formulas were presented for the two forms of integrals. Furthermore, quadratic elements are used in addition to linear ones. The quadratic element very close to the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. Especially for problems with curved boundaries, the combination of quadratic elements and linear elements can give more accurate results. |
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| Keywords: | boundary element method (BEM) nearly singular integral regularization potential problem |
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