Simple Intuitive Relations Concerning the Effect of Boundaries on the Stability of the FDTD Method

Simple intuitive relations are derived to study the effect of some boundaries on the Courant-Friedrich-Levy number (CFLN) in the finite-difference time-domain method. A novel von-Neumann stability analysis is proposed to study the effect of perfect electric conductor, perfect magnetic conductor, and perfect electromagnetic conductor boundaries on the CFLN. Also, Gershgorin's theorem is applied to determine the CFLN at the interface between two dielectrics. Studies show that the aforesaid boundaries do not restrict the CFLN of the computational space.