Collocation Spectral Method for Numerical Computation of Electric Potential Distribution Along Polluted Insulator

This article presents a new numerical computation code based on the collocation spectral method (CSM) to solve the partial differential equation (PDE) describing the potential distribution along a polluted insulator. The pollution on insulator surface is modeled by a uniform thin layer. The results of the electric potential distribution obtained by CSM are compared with those of the finite-difference method (FDM), the finite-element method (FEM), and the analytical solution. The accuracy of this method in terms of maximum (error) is discussed. Based on the newly developed code, the influence of physical parameters of the insulator model, such as the relative permittivity, surface conductivity, and insulator thickness, on the electric potential distribution is investigated.