High-voltage field computation using bi-cubic surface splines

Integral equation methods are used to compute the electric field stress on high-voltage arrangements. This paper combines the geometric description of surfaces, using bi-cubic spline functions on individual patches, with the boundary element method for calculating three-dimensional electrostatic fields. After the calculation of spline function coefficients from a given geometric design, the electric boundary conditions of electrode and dielectric parts are applied. Numerical integration by means of Gaussian quadrature leads to a linear system of equations, determining the charge density on the surface elements. This solution is used to calculate the potential and field strength on the electrode or insulator contour. The accuracy of the method is illustrated by an example.