The Gauss-Seidel iteration method as a tool for solving physical fields to obtain breakdown voltage for low pd values

This article deals with the possibilities of implementing the Gauss-Seidel iteration method (hereinafter referred to as the GSI method) along with the finite difference method to solve stationary and non-stationary inhomogeneous fields in 2D and 3D space. The main goal is to create a numerical algorithm for deriving the corona inception voltage (U
i
) between two electrodes. First, the GSI method is described step by step on a simple 2D example of an electrostatic field. The 3
^rd
part provides a comparison of the results of the previous example with the results from the Finite Element Method (FEM) solver. The 4
^th
part contains an overview of other problems solved by the GSI method: the so-called triple junction problem, the temperature field of two insulated conductors, the extension into 3D space, and finally extension into 2D, or 3D space, with the time domain. The 5
^th
and 6
^th
chapters provide a rough preview of two Townsend discharge occurrence simulations in the air environment. The conclusion section summarizes the shortcomings and advantages of the GSI method and the two mentioned approaches for T. discharge simulations.