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.
Citation: 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.

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

  • Received Date: 2001-11-27
  • Rev Recd Date: 2003-04-15
  • Publish Date: 2003-10-15
  • 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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  • [1]
    Brebbia C A, Telles J C, Wrobel L C. Boundary Element Techniques[M].Berlin, Heidelberg:Springer-Verlag, 1984.
    [2]
    Ghosh N, Rajiyah H, Ghosh S, et al. A new boundary element method formulation for linear elasticity[J]. JAppl Mech, 1986,53(1) :69-76.
    [3]
    Huang Q, Cruse T A. Some notes on singular integral techniques in boundary element analysis[J].Internat J Numer Methods Engrg, 1993,36(3) :2643-2659.
    [4]
    Tanaka M, Sladek V, Sladek J. Regularization techniques applied to BEM[J].Appl Mech Rev,1994,47(10) :457-499.
    [5]
    牛忠荣,王秀喜,周焕林.边界元法计算近边界点参量的一个通用算法[J].力学学报,2001,33(2):276-283.
    [6]
    牛忠荣.边界元法中奇异积分问题的研究及其在固体力学中的应用[D].博士学位论文.合肥:中国科学技术大学,2001.
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