Rapid Calculation of Electrostatic Green’s Functions in Layered Dielectrics

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.