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