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A fast algorithm is proposed to calculate the lightning horizontal electric field over a lossy ground.

The lightning horizontal electric field in frequency domain is approximated by a number of piecewise cubic polynomial functions by using the proposed adaptive Hermite strategy. To utilize the Hermite strategy, the frequency domain spectrum and its derivative with respect to frequency are required. The integral kernel of the derivative appears singular along the real axis. To overcome this singularity and accelerate the calculation, a new integration path is proposed. With the help of the Hermite interpolation model and the new path, the lightning horizontal electric field in time domain can be obtained rapidly.

The singularity problem has been overcome with the new integration path and the adaptive Hermite strategy proposed in this paper is at least 50 times faster than the one using the equally spaced sampling approach.

The adaptive Hermite approach can be a good candidate for fitting a wideband frequency domain response and the revised new integration path can be utilized when the calculation of the generalized Sommerfeld integral (GSI) or its derivative with respect to frequency is involved.