Application of wavelets on the interval to numerical analysis of integral equations in electromagnetic scattering problems

The wavelet expansions on the interval are employed for solving the problems of the electromagnetic (EM) scattering from two-dimensional (2-D) conducting objects. The arbitrary configurations of scatterers are modeled using the boundary element method (BEM). By using the wavelets on the interval as basis and test functions, a sparse matrix equation is generated from the integral equation under study. The resulted sparse matrix equation allows the use of sparse matrix solvers or multi-level iterations for rapid solution. The utilization of wavelets on the interval circumvents the difficulties in the application of the wavelets on the real line to finite interval problems, and has no periodicity constraint to the unknown function that is usually imposed by periodic wavelets. Numerical examples are provided and compared with the previously published data or other methods.