Numerical models for computing low-frequency electromagnetic fields can contain spatial 2D finite elements, which are numerically most demanding due to problem of singularity. In this paper, an advanced time-harmonic quasistatic surface charge simulation method for computation of scalar electric potential and electric field intensity distribution is presented. Subparametric spatial 2D finite elements with an arbitrary number of nodes for description of surface charge density distribution are developed. The problem of singularity that occurs in the double 2D integration over these elements is solved using an originally developed advanced numerical integration based on 2D Gaussian quadrature. Self and mutual coefficients of spatial 2D finite element nodes are numerically computed and included in the system of linear equations for surface charge density distribution computation. The accuracy of the computer program, based on the presented model, is shown in the chosen numerical example with known analytical solution. Numerical model and advanced integration presented herein could be easily extended to non-homogeneous regions and multilayer problems using the image method. 
A surface charge simulation method based on advanced numerical integration