Finding proper orthogonal wavelets to solve electromagnetic scattering problems

Abstract

A novel concept of "visible energy" is proposed and its magnitude is valuable information for determining whether the chosen orthogonal wavelet is proper in solving a electromagnetic scattering problem. With the properly chosen wavelets for the targeting problem, the (transformed) wavelet-domain impedance matrix can be sparsified effectively for solving electromagnetic integral problems. It is found that for the large matrix size using the wavelets with smaller visible energy will lead to a greater sparsification of the matrix. A simple scattering problem of circular cylinder is considered to show the validity of our findings.