Generalization of the Atkinson-Wilcox Theorem and the Development of a Novel Scaled Boundary Finite Element Formulation for the Numerical Simulation of Electromagnetic Radiation

Abstract

The Scaled Boundary Finite Element Method is a novel semi-analytical method jointly developed by Chongmin Song and John P Wolf to solve problems in elastodynamics and allied problems in civil engineering. This novel method has been recently reformulated for the following categories of problems in electromagnetics: (1) Determination of Eigen values of metallic cavity structures, 2) Full wave analysis of Shielded micro-strip transmission line structures, and Very Large Scale Integrated Circuit (VLSI) interconnects, and 3) Full wave analysis of periodic structures. In this paper, a novel Scaled Boundary Finite Element formulation is developed for the numerical simulation of the time harmonic electromagnetic radiation in free space from metallic structures of arbitrary shape. The development of the novel formulation necessitates the generalization of the familiar Atkinson-Wilcox radiation series expansion so as to be applicable for arbitrary boundary circumscribing the source of radiation.