| Method of moment (MOM) is the commonest frequency domain methods in computational electromagnetics. The important keys of MOM are generalized as follows:proper choice of basis functions and test functions, skillful singularity treatment, fast matrix filling, and effective matrix inverse.Some research work has been done as follows:wavelet theory is merged into MOM, and the scattering character of different objects, materials, or frequencies is analyzed by continuous wavelet transform and discrete wavelet transform. Firstly, the wavelet theory is introduced resumptively. Secondly, periodic wavelets are applied to single and multiple scattering by electric field integral equation and magnetic field integral equation. Preconditioning method based on physical optics is presented, and it reduces the dimensions and condition number of impedance matrix. Thirdly, the radar cross section of conductors, dielectrics, and inhomogeneous scatters is computed by combined field integral equation, PMCHWT equation, and volume integral equation. Wavelet-like transform based on lifting scheme is used to sparsify impedance matrix as preconditioning kernel, and it cuts down computation complexity of iterative methods with smaller computer time.Numerical results suggest as follows:Considering the accuracy of electric current in the surface of objects, physical optics preconditioning method compared to traditional method produces the better matrix with lower dimensions by discarding lots of fictitious wavelet-basis functions. Further more, considering the same compression ratio, lifting wavelet transform compared to traditional wavelet transform saves the memory of preconditioning matrix and about half computer time. Lifting wavelet transform can be widely used in numerical computation of electromagnetic scattering or radiation problems as a preconditioning kernel.
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