Electric field calculation in composite dielectrics by first-order triangular surface charge method

Abstract

This paper describes a triangular surface charge method (TSCM) called (3,1)-TSCM, which uses curved surface elements for calculating electric fields in composite dielectrics. The boundary element utilizes a cubic shape function with nine degrees of freedom and a linear function for representing the charge density on its surface. Conventional SCMs, including the (3,1)-TSCM, show a very large relative error in the composite dielectrics where the permittivity is much higher in one medium than in the other. A modified method called the β method can suppress such relative errors, which expresses electric fields by surface charges without subtraction causing large relative errors. We have applied the β method to the (3,1)-TSCM and calculated electric fields for a spherical dielectric under a uniform field. The calculated results show that the (3,1)-TSCM improves the accuracy of the electric field by more than one order compared with the method using flat surface elements with constant charge density on each element. Furthermore, the β method completely suppresses the divergence of relative errors even when the ratio of the permittivity of two media reaches 1010. © 2001 Scripta Technica, Electr Eng Jpn, 136(1): 1–8, 2001