Numerical integration of singularities in meshless implementation of local boundary integral equations

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Meshless formulations for simply supported and clamped plate problems (2002, background): “As to the numerical computation of limits of boundary integrals over s with strongly singular kernels @U ∗=@n, recall that in general, a special technique is required [13].”
A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function (2004, methodology): “Several meshless methods have also been reported in the literature, for example, the domain-based methods including the element-free Galerkin method [2], the reproducing kernel method [3], and boundary-based methods including the boundary node method [4], the meshless local Petrov–Galerkin approach ”
Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids (2003, background): “Such an expression is appropriate ( Sladek et al., 2000 ) if the temperature is approximated by shape functions known only numerically at integration points because there is no possibility for the regularization of the integrand.”