Application of second generation wavelet transform to solution of electromagnetic integral equations

Abstract

The theory of the second generation wavelet transform was described and specific formulas for wavelet matrix transform were deduced, and finally a preprocessing technique based on the second generation wavelet transform was proposed to accelerate the solution of electromagnetic integral equation. By sparsfying the dense impedance matrix obtained by method of moments (MOM), the matrix-vector-multiplication (MVM) for iteration was sped up. To eliminate the limitation to matrix dimension when the traditional wavelet transform was used, a new preprocessing algorithm for arbitrarily dimensional matrix equations was constructed. The electromagnetic scattering analysis of different objects was completed, and the results were compared with that obtained by the analytical solution or direct MOM solution to validate the effectiveness of the proposed method. Due to its generality, the presented matrix transform technique can also be expanded to other engineering computation areas.