Novel formulations for evaluating hypersingular volume integrals over cuboid domains

Volume integral equations (VIEs) are indispensable to formulate inhomogeneous or anisotropic electromagnetic (EM) problems and cuboid meshes are preferred to discretize volume domains in some applications. In solving the VIEs, accurate evaluation for singular integrals is very essential but there is no direct method to evaluate hypersingular integrals over a cuboid domain so far. In this work, we propose some closed-form formulas for calculating those hypersingular volume integrals and they are simpler and more efficient to implement. A numerical example is presented to demonstrate the formulas and their effectiveness has been verified.