Finding proper orthogonal wavelets to solve electromagnetic scattering problems

A novel concept of "visible energy" is proposed and its magnitude is valuable information for determining whether a chosen orthogonal wavelet is proper in solving an electromagnetic scattering problem. With 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 large matrix size, using wavelets with smaller visible energy will lead to a greater sparsification of the matrix. A simple scattering problem of a circular cylinder is considered to show the validity of our findings