Coupled stability analysis for the open-region finite-difference time-domain simulations

When the FDTD method is used to solve open-region electromagnetic problems, the mesh-truncation technique, or the absorbing boundary condition (ABC), can introduce another source or mechanism of instability. In this work, we present a new boundary condition stability analysis method, coupled stability analysis (CSA). This analysis is based on the fundamental assumption that absorbing boundary conditions are not perfect, and therefore, generate waves that reflect back intoo the computational domain. A an important consequence of this analysis, and contrary to earlier conjectures, we show that Higdon's absorbing boundary condition of order 3 (and possibly, higher orders) to be unconditionally unstable. The theoretical predictions of the CSA are supported by previous numerical findings and several numerical experiments presented here.