Fast Evaluation of the Horizontal Electric Field of Lightning With Cooray–Rubinstein Formula in Time Domain Using a Piecewise Quadratic Convolution Technique

The Cooray-Rubinstein formula has been widely utilized for evaluating the horizontal component of the electric field generated by a lightning return stroke. A fast time-domain implementation of Cooray-Rubinstein formula in time domain, by means of the piecewise quadratic convolution technique and the use of a quadrature routine of a truncated integral instead of polynomial approximations of the Bessel functions, is presented in this paper. The advantages of the proposed approach can be summarized as follows. First, the issue of the numerical overflow and the cancellation error for calculating the lightning horizontal electric field is avoided; second, the horizontal electric field of a lightning can be evaluated quickly, because the convolution has been expressed in a closed-form expression. The numerical examples demonstrate the efficiency and validity of the proposed approach.