Rapid calculation of electrostatic Green's functions in layered dielectrics

Abstract

This paper introduces a new method for the development of closed-form spatial Green's functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green's function to overcome the tedious numerical integration of the Fourier-Bessel inverse transform that is required to generate the Green's function in the space domain. Through a special representation of the finite-difference form of the spectral Green's function, the Fourier-Bessel transforms can be obtained in closed form in terms of modified Bessel functions of zeroth order. Numerical examples from the calculation of the capacitance matrix of multi-conductor systems in layered dielectrics are used to demonstrate the validity of the generated closed-form Green's functions and their computer implementation.