Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems

ZHOU Huan-lin; NIU Zhong-rong; WANG Xiu-xi

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(10): 1069-1074

ZHOU Huan-lin, NIU Zhong-rong, WANG Xiu-xi. Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems[J]. Applied Mathematics and Mechanics, 2003, 24(10): 1069-1074.

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Regularization of Nearly Singular Integrals in the Boundary Element Method of Potential Problems

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

Received Date: 2001-11-27
Rev Recd Date: 2003-04-15
Publish Date: 2003-10-15

Abstract

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.
- BEM,
- nearly singular integral,
- regularization,
- potential problem

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References(6)

References

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