Three-dimensional unconditionally-stable operator-splitting FDTD methods

At present, conventional alternating-direction implicit finite-difference time-domain (ADI-FDTD) method is very popular because it is characterized by unconditional stability. However, conventional ADI-FDTD method is only second-order accurate in time, which means that numerical dispersion will deteriorate severely as time step is chosen to be large. In this letter, the concept of exponential evolution operator combined with operator splitting is introduced into the solution of 3D Maxwell´s equations, from which new unconditionally-stable FDTD methods are derived. The new methods only need to solve uncoupled 1D equations, which is very flexible. In this letter, those new methods are called the OS-FDTD methods for simplicity.