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

Abstract

SUMMARYThis 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 E method can suppress such relative errors, which expresses electric fields by surface charges without subtraction causing large relative errors. We have applied the E 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 E method completely suppresses the divergence of relative errors even when the ratio of the permittivity of two media reaches 10

Electric field calculation in composite dielectrics by curved surface charge method based on electric flux continuity condition

“…However, the number of unknowns per element increases, and hence more boundary conditions are necessary, which gives rise to specific problems in the SCM applied to composite dielectric calculations [4,5]. The necessary boundary conditions are obtained by using atypical shape functions [3,5] as explained above, or by the combined use of conforming and nonconforming elements.…”

“…However, when typical shape functions such as 6-DOF second-order functions and 10-DOF thirdorder functions are employed, there are specific problems in the SCM when applied to composite dielectric calculations [5]. Therefore, shape modeling is implemented by special shape functions such as 9-DOF third-order functions [5,8] and 4-piece cooperative 9-DOF third-order functions [3], which provide better shape modeling.…”

“…As regards shape modeling, it has already been shown that the introduction of a 3D shape representation function into SCM contributes to better accuracy of boundary modeling, and, therefore, of electric field calculation [5]. However, such an approach has not yet been applied to Φ s .…”

“…It is common knowledge that with the surface charge method (SCM), the surface charge density distribution on a media interface is expressed by a piecewise function, which is then used in combination with boundary conditions to calculate the static electric field. The authors have conducted extensive research aiming at improving the accuracy of field calculation in dielectrics by using the SCM with triangular segments [2][3][4][5][6][7]. In particular, regarding the representation of boundary conditions on dielectric boundaries, a method called Φ s based on the electric flux continuity condition has been proposed, offering a substantial improvement of calculation accuracy compared to conventional point matching [6].…”

Electric Field Calculation for Composite Dielectrics by a Curved Surface Charge Method with Non-conforming Charge Representation

“…Although it has a long history of application, it is not yet fully developed as a reliable and accurate method, in particular, in composite dielectrics and three-dimensional conditions. We have been improving the accuracy of SCM in these conditions (1) , (2) by applying various computational techniques relating to (i) representation of surface profiles, (ii) expression of charge density on boundary surfaces, and (iii) formulation of boundary conditions. In this paper, we demonstrate the usefulness of a curved surface charge method with non-conforming charge representation.…”