Abstract
This paper describes the mapping theory which is useful for the analysis of the electric field in three-dimensional anisotropic media. The mapping relations of various electric quantities between two anisotropic media with charge distribution are presented. In this mapping, an anisotropic medium can be transformed to an equivalent isotropic one. The simple isotropic mapping function is presented, and it is made clear that the isotropic permittivity can be determined arbitrarily and the convenience is caused by a similarity transformation. Furthermore, it is shown that the mapping conserves the field continuity on the boundary when one mapping function is applied to the compound regions consisting two or more different anisotropic media. In addition, the isotropic mapping for the compound region is discussed and the mapping function in some limitations is presented.
