Singular integrals and boundary elements Original Research Article

The aim of this paper is to give a view on mathematical singularities involved in the BEM formulations. The regularized integral representations (of the primary and secondary fields) and boundary integral equations (ordinary and derivative BIEs) demonstrate the possibility of removing the non-physical singularities of various kinds from the BEM formulations. The continuity requirements on the approximation of physical boundary densities and the boundary geometry are discussed together with the consequences of insufficiently smooth approximations. The modified Overhauser elements are developed in the two-dimensional case.