Efficient Evaluation of High-Order Pulse Green's Functions for Bodies of Revolution Problems

In this work, high-order approximations of the pulse Green's functions (PGFs) and their gradient, referred to as the PGFs of the first and second kind, respectively, are presented. A generalized approach is developed to obtain the closed-form expressions for the Nth-order PGFs. The proposed formulations are derived using Taylor series expansions to overcome the computational bottlenecks associated with traditional methods based on numerical integrations. A recursive relation is obtained by integrating higher-order terms along the body-of-revolution (BOR) generating curve, leading to analytical expressions for PGFs of arbitrary orders. These formulations eliminate the λ/10 limitation on the distance between two points along the generatrix, allowing flexible control between accuracy and efficiency. The computational accuracy and efficiency of the proposed analytical approach are demonstrated through numerical examples to highlight its applicability in the method of moments analysis of electrically large BOR objects with complex geometries.