High-Discretization Method of Moments for Capacitance Calculation: A Cube and a Hollow Cylinder

TL;DR

This paper presents a high-discretization method using the method of moments to accurately calculate capacitances of a cube and hollow cylinder, highlighting the impact of discretization on accuracy and computational efficiency.

Contribution

The paper introduces a high-discretization MOM approach for capacitance calculation, demonstrating optimal discretization levels and validating results against theoretical and experimental data.

Findings

Capacitance of the cube peaks at a certain discretization level.

Higher discretization does not always improve accuracy.

Results for the hollow cylinder agree with theoretical and experimental values.

Abstract

This paper employs the method of moments (MOM) to calculate the capacitances of a cube and a hollow cylinder. For the cube, each face was divided into a maximum of 600 x 600 sub-areas. By fully exploiting the geometric symmetry between sub-areas and incorporating parallel computing, computational resources were significantly conserved. Our results show that the calculated capacitance of the cube first increases and then decreases as the number of sub-areas increases. When each face was divided into 90 x 90 sub-areas, the capacitance of the unit cube (with an edge length of 1 m) reached a maximum reference value of 73.519014 pF. This indicates that higher accuracy cannot be achieved merely by indefinitely increasing the number of discretized sub-areas. Subsequently, the method was applied to compute the capacitance of a hollow cylinder. The results were compared with numerical solutions based on Lekner's theoretical formula and Cavendish's experimental values, showing good agreement among the three.