{'fraction_non_alphanumeric': 0.01904761904761905, 'fraction_numerical': 0.0, 'mean_word_length': 5.661971830985915, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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.