Extended Kelvin Transformation for Solving Radiating Electromagnetic Fields

Abstract

This paper presents an extension of the Kelvin transformation for high-frequency electromagnetic problems. The Kelvin transformation is a coordinate transformation that maps infinite space to a finite space, acting as a conformal transformation of Maxwell’s equations. We apply concepts of differential geometry to derive the material constant’s metric and spatial dependence in the exterior domain, which was originally proposed for low-frequency eddy current problems. This paper extends the conformal transformation concept to high-frequency problems by introducing a Perfectly Matched Layer (hereafter referred as to PML) in the exterior domain. This technique makes it easy to apply a simple Maxwellian PML.