Fast evaluation of the Cooray–Rubinstein formula in time domain via piecewise recursive convolution technique

Abstract

The Cooray-Rubinstein formula has been widely used for evaluating the horizontal component of the electric field generated by a lightning return stroke over a lossy ground. An accurate and efficient time domain method is presented in this study, by means of piecewise recursive convolution. The recursive convolution is achieved by expressing the kernel function of the ground surface impedance by a piecewise exponential function, in which the integral form of the modified Bessel function of the first kind is evaluated using the trapezoidal numerical integration. Since the time-domain analytical expression of the ground surface impedance kernel function has been adopted, the computational error can be directly controlled within a reasonable tolerance. The validity and efficiency of the proposed method are demonstrated by the extensive comparisons with the method in other literature.