A novel concept for finding proper orthogonal wavelets effectively to solve a large object scattering problem

Abstract

[1] A novel concept of "visible energy" is proposed, and its magnitude is shown to be valuable information for determining whether the chosen orthogonal wavelet is proper in solving a large object 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. Visible energy is defined as the energy of all dilations of a single mother wavelet for an arbitrary translation in the spectral domain over the entire "visible region." It is found that for large matrix sizes, using wavelets with smaller visible energy will lead to a greater sparsification of the matrix. Numerical examples considering various scatterers with different shapes such as a circular cylinder, an L-shaped scatterer, and a duct show the validity of our findings.