Efficient Evaluation of PGF Based on High-Order Taylor Expansions

This work is concerned with the numerical computation of the pulse Green’s function (PGF), which arises from the electromagnetic radiation and scattering of bodies of revolutions (BoR). The focus is on improving the computational efficiency to offer better service for problems involving large-scale BoRs. Computational electromagnetics for the radiation and scattering problems of BoRs is one of the typical problems that is widely used in electromagnetic engineering. The method of moment (MoM) is an effective numerical method to solve the problems of BoR. In order to improve the computational efficiency, many fast algorithms based on the MoM have been proposed. The computations involving the Green’s function are important in the MoM since it consumes a dominating part of the computational sources. Either the modal Green’s function (MGF) or the PGF is required to be evaluated in BoR-MoM. The methods based on MGF are invested and used more widely than PGF. However, for a large-scale problem, the evaluations of MGF require an excessive number of recurrences to avoid significant loss of precision, or the forward and backward recurrences should incorporate with each other to keep the algorithms stable. The integration of PGF can be obtained in closed-form with respect to the length of generatrix
$t$
based on Taylor expansion to get rid of the heavy computations of recurrences. The lack of research studies on PGF is mainly because it requires the distance between two adjacent discrete points on the generatrix to be less than (or equal to) a tenth of the wavelength of the incident field. In this article, the spectral accuracy for the computation of PGF is achieved based on high order Taylor expansions. The restriction of “less than (or equal to) a tenth of the wavelength of the incident field” is overcome. Numerical simulations are carried out to show the significant savings in computational expenses.