Distance transformation for the numerical evaluation of near singular boundary integrals with various kernels in boundary element method

Abstract

The accurate numerical solution of near singular boundary integrals was an issue of major concern in most of the boundary element analysis next to the singular boundary integrals. The problem was solved in this paper by a kind of non-linear transformation, namely, the distance transformation for the accurate evaluation of near singular boundary integrals with various kernels for both the two- and three-dimensional problems incorporated with the distance functions defined in the local intrinsic coordinate systems. It is considered that two effects play the role in the transformation. They are the damping out of the near singularity and the rational redistribution of integration points. The actual numerical computation can be performed by standard Gaussian quadrature formulae and can be easily included in the existing computer code, along with its insensitivity to the kind of the boundary elements. Numerical results of potential problem were presented, showing the effectiveness and the generality of the algorithm, which makes it possible, for the first time, to observe the behaviors of various boundary integral values with numerical means, when the source point is moving across the boundary with fine steps.