Adaptive Gaussian quadrature over surface splines in high‐voltage field computation

Integral equation methods are very often used for high‐voltage field computation. This paper describes an adaptive Gaussian quadrature method for solving potential and field related integrals. Based on computer‐aided design, the high‐voltage configuration is modelled using bi‐cubic spline functions for the description of the boundary surfaces. This problem definition requires a numerical solution of the governing integral equations. Standard Gauss‐Legendre quadrature is improved by an adaptive approach. The describing surfaces are sub‐divided under distance‐dependant aspects. Hence, different rules of Gaussian quadrature are examined and compared to analytically obtained results. The solution is used to compute the potential and field strength on the electrode or insulator contour. The accuracy and the speed‐up of the new method is demonstrated by several calculations.