Wavelet-like bases for thin-wire integral equations in electromagnetics

Abstract

In this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain.The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform.The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation.The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis transform is used to sparsify the moment matrix.In particular, dyadic and M-band wavelet transforms have been adopted, so generating different sparse matrix structures.This leads to an efficient solution in solving the resulting sparse matrix equation.Moreo ver, a wavelet preconditioner is used to accelerate the convergence rate of the iterative solver employed.These numerical features are used in analyzing the transient behavior of a lightning protection system.In particular, the transient performance of the earth termination system of a lightning protection system or of the earth electrode of an electric power substation, during its operation is focused.The numerical results, obtained by running a complex structure, are discussed and the features of the used method are underlined.