On the use of wavelet transform for efficient iterative solution of the electromagnetic models in lightning studies

The lightning return-stroke channel is commonly approximated as a straight thin-wire antenna over perfect ground for which the numerical solution of the governing electric field integral equation by the conventional method of moment is prohibitively slow. In this paper, first, a fast discrete wavelet transform is used to compress the Fourier spectrum of the excitation. An appropriate predefined wavelet packet basis transform is, then, employed to effectively sparsify the resulting matrix equations for the entire frequency range of interest. Finally, the conjugate gradient method with wavelet-based preconditioning is exploited to reduce the memory space and processor cycles of the simulation process