An explicit and unconditionally stable FDTD method for 3-D electromagnetic analysis

In this paper, an explicit and unconditionally stable finite-difference time-domain (FDTD) method is developed for electromagnetic analysis. It is stable for an arbitrarily large time step irrespective of space step, and accurate for a time step solely determined by accuracy. The method retains the strength of the conventional explicit FDTD in avoiding a matrix solution while eliminating the conventional FDTD's shortcoming in time step. Numerical experiments in both 2-D and 3-D simulations have demonstrated its superior performance in stability and efficiency without losing accuracy. The proposed method successfully generates stable and accurate results with a time step 10
¹³
times larger than that allowed by the conventional FDTD in an example where the time step required by accuracy is 10
¹³
times larger than that permitted by stability.