A Novel Green’s Function Decomposition Method for Fast Computational Electromagnetics Algorithms

An efficient decomposition of the fundamental scalar Green’s function has been proposed in this paper for potential fast Computational Electromagnetics (CEM) algorithms: via a novel Numerical Singular Integral (NSI) method that the authors developed, the Fourier spectrum of the scalar Green’s function can be decomposed into 6 parts with physics meaning: 3 parts inside the k circle corresponding to the propagating waves, and 3 parts outside the k circle corresponding to the evanescent waves. Then the corresponding partial Green’s functions can be effectively evaluated through conventional numerical quadrature integral rules, either in the spatial domain or in the spectral domain. After that, efficient CEM algorithms can be developed by dealing with these 6 partial Green’s functions separately and adaptively in either the Fourier spectral domain or the spatial domain. Numerical validation of the Green’s function decomposition has been performed in the popular triangular domain.