High accuracy calculation of electric field in composite dielectric system by improved 3-D boundary charge method

Abstract

In this paper, we propose an improved three-dimensional (3-D) boundary charge method for a composite dielectric system where there is a great difference in magnitude of the permittivity between neighboring dielectric materials. The method is based on the idea that the whole region of the composite dielectric system is divided into two regions; one being the region H containing the dielectric material of high permittivity ε H and the other being the region L containing the dielectric material of low permittivity ε L. The boundary of division is selected so as to coincide with the interface between ε H and ε L. We then arrange surface charge densities on both sides of the interface between ε H and ε L as well as on every conductor-to-dielectric interface in respective regions of H and L. The key point of our improved method is that when we calculate the electric field in the region H, for example, we use only the surface charge densities in the same region and do not use those in the region L. When we calculate the electric field in the region L, a similar rule is applied. In order to determine the surface charge density on every interface we utilize boundary conditions for potential and electric field at every interface. This procedure eliminates the loss of numerical accuracy arising from cancellation in addition, and we have succeeded in improving numerical accuracy even when there is a great difference in magnitude of the permittivity between neighboring dielectric materials.