A direct approach for solving 3D EFIE with double gradient of the Green's function

In this paper, a direct approach for solving the 3D EFIE including the double gradient of the Green's function (second form) is developed. The direct solution for the equation is thought to be prohibitive due to the existence of super-hyper singularities in the kernel for self-interaction terms. The closed-form expressions for these super-hyper singular integrations are derived in a limiting sense and the solving of the equation directly is made possible. Moreover, analytical formulas for the weakly singular integrations in the limiting sense (i.e. w₀ ne 0) are derived. These formulas can be used to calculate the near-interaction terms exactly no matter how close to the source patch the observation point is. This approach also allows one to represent the current using pulse-like bases with simplicity and flexibility, albeit in a lower-order approximation. A higher-order approximation for the current can be considered in the future