New identities for fundamental solutions and their applications to non-singular boundary element formulations

Based on a general, operational approach, two new integral identities for the fundamental solutions of the potential and elastostatic problems are established in this paper. Non-singular forms of the conventional boundary integral equations (BIEs) are derived by employing these two identities for the fundamental solutions and the twoterm subtraction technique. Both the strongly(Cauchy type) and weakly-singular integrals existing in the conventional BIEs are removed from the BIE formulations. The existence of the non-singular forms of the conventional BIEs raises new and interesting questions about the smoothness requirement in the boundary element method (BEM), since the two-term subtraction requires, theoretically, C continuity of the density function, rather than the C continuity as required by the original singular or weakly-singular forms of the conventional BIEs. Implication of the non-singular BIEs on the smoothness requirement will be discussed in this paper.