On the low-frequency breakdown of FDTD

In this work, we find the FDTD-based time-domain simulation breaks down at low frequencies in both explicit and implicit time marching schemes. This breakdown also exists in the other time-domain methods since the root cause is finite machine precision. A rigorous and fast method is developed in an unconditionally stable and also explicit FDTD method to solve the low-frequency breakdown problem. Numerical simulations of transient phenomena with arbitrarily low input frequencies have validated the proposed method.