A Three-Dimensional Unconditionally-Stable FDTD Method Based on Split-Step Scheme and Crank-Nicolson Scheme

A new three dimensional split-step finite-difference time-domain (FDTD) method bases on Crank-Nicolson scheme is presented, which provides simple algorithm implementation and new splitting forms along the x, y and z coordinate directions. Through three sub-steps, the corresponding scheme translates a 3-D problem into three 1-D problems to reduce computational complexity. The proposed method is proven to be unconditionally stable and has second-order accuracy in time and space. In the application of a cavity, the proposed method produces 10% reduction of the run time than the alternating-direction implicit (ADI)-FDTD method and 35% than the split-step (SS)-FDTD (2,2) method.