Salvadori A. Analytical integrations in 3D BEM: preliminaries

Abstract This work provides a preliminary contribution in the context of analytical integrations of strongly and hyper singular kernels in boundary element methods (BEMs) in 3D. It concerns the integral of 1=r3 over a triangle in R3, that plays a fundamental role in BEMs in 3D, especially for the Galerkin implementation. Because the existence of the aforementioned integral depends on the position of the source point, all significant instances of the position of the source point will be considered and detailed. For its interest in the context of BEM, the integral is also considered in the more general sense of finite part of Hadamard