Some Improvements of Numerical Techniques for the Surface Charge Method

Abstract

This paper describes some techniques applied to the Surface Charge Method (SCM). The toroidal tetragonal element is introduced to approximate toroidal surfaces. To demonstrate its superiority to the parabolic triangular element, the field in a layered toroidal capacitor is evaluated by SCM, and the results are compared to the accurate analytical solution. Some analytical and semi-analytical formulas are presented, which are suitable for the computation of diagonal and near-diagonal coefficients of the coefficient matrix. Presented techniques improve the accuracy and reduce computation time for assembly of system of algebraic equations.