Reduction of singular surface integrals to non-singular line integrals in integral equations involving non-parallel surface elements

A novel procedure is presented for the evaluation of integrals involving singular Green function and Rao-Wilton-Glisson basis functions with arbitrary mutual non-planar geometrical configuration which appear in surface integral equations representation of Maxwell equations. The proposed procedure constitutes a generalization of our previously reported result valid for planar geometries. The method employs a suitably constructed representation of the Helmholtz equation Green function in terms of an differential operator acting on an auxiliary function which allows one to reduce four-dimensional surface integrals with singular integrands to line integrals over triangle edges with regular integrands. Advantages of our approach include simplicity and high accuracy at a computational cost considerably lower than for previously considered methods, such as the singularity subtraction technique.