Numerical simulation of electromagnetic fields radiated by lightning return stroke channels: a wavelet-based approach

The antenna theory model is widely employed to numerically simulate the propagation of current wave along lightning return stroke channels and compute the radiated electromagnetic fields. In this model, the channel is approximated as a vertically straight or a horizontally bent thin-wire antenna above perfectly conducting ground for which the numerical solution of the governing electric field integral equation in frequency domain by the conventional method of moment is prohibitively slow. This paper proposes an efficient algorithm to substantially reduce the computation time of the numerical process for the entire frequency components of the excitation current. In this algorithm, a class of predefined wavelet packet transform is first used to effectively sparsify the resulting moment matrix equations. A proper iterative solver is then utilized to take the full advantages of manipulatory sparse matrices. To accelerate the construction of the original moment matrix, the reciprocal closed-form mutual impedance of sinusoidal electric dipoles and the symmetry of the model are fully exploited. A good agreement is observed with computed data found in technical literature while the overall computational time is reduced remarkably. Index Terms--Antenna theory (AT) model, lightning return stroke, method of moment (MoM), sinusoidal dipoles, thin-wire electric field integral equation (EFIE), wavelet packet transform.