On the computation of nearly singular integrals in 3D BEM collocation

In this paper, we propose an efficient strategy to compute nearly singular integrals over planar triangles in R3 arising in boundary element method collocation. The strategy is based on a proper use of various non-linear transformations, which smooth or move away or quite eliminate all the singularities close to the domain of integration. We will deal with near singularities of the form 1/r, 1/r 2 and 1/r 3, r =x−y being the distance between a fixed near observation point x and a generic point y of a triangular element. Extensive numerical tests and comparisons with some already existing methods show that the approach proposed here is highly efficient and competitive.