on some Techniques of Treating Weakly Singular Integrals

Abstract

The weak singularity issue arises in the boundary integral equations either directly or as a result of reducing the hypersingularity to at worst weak singularity by using some regularization formulae. Here we show some analytic and numerical techniques to deal with the weak singularity phenomenon of the boundary integral equations. These powerful techniques include the logarithmic Gaussian quadrature, subtraction of singularity and coordinate transformations that are formulated in such a way that the singularity is removed.