Electric field calculation in composite dielectrics by a curved triangular surface charge method

Abstract

AbstractThis 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