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

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.