Absorbing boundary conditions for the TLM method

The numerical behavior of different absorbing boundary conditions when applied to the transmission-line modeling (TLM) method is presented. These conditions may be classified into three different groups according to the way they are derived. The first group is obtained by discretizing one-way analytical conditions derived for the analytical wave equation. The second group is a set of discrete conditions directly obtained for the discrete wave equation. The last group is based on appropriate reflection coefficients derived purely from transmission-line theory. Because of their different behaviors, the numerical study is explicitly carried out for both two- and three-dimensional free-space scattering problems