General distance transformation for the numerical evaluation of nearly singular integrals in BEM
J.H. Lv, Y. Miao and H.P. Zhu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 91, No. 2, pp. 101-117, 2013
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Keywords Boundary element method, Nearly singular integrals, Numerical integration, Distance transformation technique
Abstract The accurate and efficient evaluation of nearly singular integrals is one of the major concerned problems in the implementation of the boundary element method (BEM). Among the various commonly used nonlinear transformation methods, the distance transformation technique seems to be a promising method to deal with various orders of nearly singular integrals both in potential and elasticity problems. In this paper, some drawbacks of the conventional distance transformation, such as the sensitivity to the position of projection point, are investigated by numerical tests. A general distance transformation technique is developed to circumvent these drawbacks, which is aimed to remove or weaken the limitations of the projection point. Several numerical examples are presented for both straight and curved line elements to validate the accuracy and efficiency of presented method.
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