A New Approach for Numerical Evaluation of High Order 3D Singular Boundary Integrals

In this paper, a new approach is presented for numerical evaluation of three-dimensional (3D) weakly, strongly, hyper- and super-singular boundary integrals which exist in the Cauchy principal value sense. In the approach, the singularities involved in integration kernels are analytically removed based on the use of the radial integration method and expansions of the non-singular parts of the kernels as power series with respect to the local distance in the intrinsic coordinate system. One of the features of the approach is that the global distance between source and field points is exactly expanded as the power series in local one for linear and high order boundary elements. This expansion is different from existing approaches in which the Taylor series is used to approximate the distance and other quantities. Some examples are provided to verify the correctness and efficiency of the presented approach.