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

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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

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