On numerical approximation of electrostatic energy in 3D (Q1276219)

The authors discuss numerical methods for the calculation of electrostatic energy associated with a volume charge density distribution. The particular cases considered in detail are when the domain of the charge distribution is a compact convex polyhedron and when the density is a polynomial function in Cartesian coordinates methods associated with integral geometry are used to reduce the six dimensional domain of double integration to a two dimensional domain. The work is extended to show how the mutual electrostatic energy may be calculated. The results of numerical work are given for a variety of quadratic schemes, and the results of applying these to calculate the energy (in effect the capacity) of a unit cube. Much of the work is contained in the references.