Integral Equations for Electrostatics Problems with Thin Dielectric or Conducting Layers

Integral equations for the electric charge on continuous, arbitrarily thin, dielectric or conducting layers in axially symmetric geometries have been derived. When discretized, these equations become Boundary Element Method (BEM) equations for the charge. While the only boundary conditions enforced are continuity of potential and normal electrical displacement, the result is shown to be consistent with the boundary conditions used in the Charge Simulation Method (CSM) and the Finite Element Method (FEM) formulations of the problem. The method has the advantages over CSM that it requires only half the number of unknowns and it can be used to model the fields near the thin layer without using large numbers of unknowns. It has the advantage over FEM that only the thin layer surface need be discretized rather than the entire volume.