Loop-star decomposition of basis functions in the discretization of the EFIE

A general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder. The proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions. The completeness of the loop-star basis is discussed, employing the presented scheme; the issue of the irrotational property of the nonsolenoidal functions is addressed.