Evaluation of hypersingular volume integrals over a cylindrical domain in meshless methods

In the meshless scheme for solving volume integral equations (VIEs), one needs to evaluate hypersingular integrals over a small cylindrical domain excluded from the whole domain for the sake of regularizing integrands. Those integrals can be evaluated semi-numerically but the implementation may not be convenient. In this work, we present some new formulas which are purely analytical for those integrals so that their evaluation can be greatly simplified. A numerical example for electromagnetic (EM) scattering is presented to demonstrate the new formulas.