A new smoothing strategy for computing nearly singular integrals in 3D Galerkin BEM

AbstractIn this paper we propose an efficient strategy to compute nearly singular integrals over planar triangles in R3, arising in 3D Galerkin BEM. The strategy is based on a proper use of various nonlinear 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 and 1/r3, r=‖x−y‖ being the distance between two generic points x and y lying on triangles which are disjoint, but very close to each other. The approach proposed here is demonstrated by numerical experiments