New radiation boundary condition for the finite difference time domain method

In the analysis of antennas and scattering problems by the finite difference time domain (FDTD) method, the dimensions of the problem space are primarily determined by the quality of the radiation boundary condition (RBC) that is used to truncate the computational grid. Higher order boundary conditions give better performance when used in conjunction with pulse type sources. Unfortunately, they are less efficient when applied to scattering problems as shown by Blaschak and Kriegsmann (1988). This suggests that the current one-way wave equation approximations are overlooking an important aspect of the problem. We believe that the problem resides in the inability of the higher order approximations to deal with the evanescent part of the field. Since this evanescent part is much more prominent in scattering type problems, especially at low frequencies, this would explain the apparent failure of the higher order conditions in those cases. We propose a boundary condition that takes into account evanescent as well as non-evanescent plane waves and prove that this new RBC gives excellent results in both scattering and pulse-type problems. We restrict ourselves to two-dimensional problems but our approach can be extended to 3D problems as well.