Calculation of 3-dimensional fields in a medium with several dielectrics

An analytical-numerical method for computing electric fields in 3-dimensional geometries in heterogeneous media, consisting of several dielectric regions within which there are several conductors to known or floating potentials, is introduced. The method is applicable to those geometries in which the conductors and dielectric materials have forms that can be modeled by spheres, prolate spheroids, oblate spheroids or torus, which is very common in HV and EHV systems with the purpose of reducing or eliminating corona phenomena. The method is based on an analytical function constructed for the electric potential, from a limited development of harmonic functions in a coordinate system appropriate to the form of the conductors and dielectric regions in the medium