A generalized higher order finite-difference time-domain method and its application in guided-wave problems

In this paper, a (2M, 4) scheme of the, finite-difference time-domain (FDTD) method is proposed, in which the time differential is of the fourth order and the spatial differential using the discrete singular convolution is of order 2M. Compared with the standard FDTD and the scheme of (4, 4), the scheme of (2M, 4) has much higher accuracy. By choosing a suitable M greater than or equal to 2, the (2M, 4) scheme can arrive at the highest accuracy. In addition, an improved approximation of the symplectic integrator propagator is presented for the time differential. On one hand, it can directly simulate unlimited conducting structures without the air layer between the perfectly matched layer and inner structure; on the other hand, it needs only a quarter of the memory space required by the Runge-Kutta time scheme and requires one third of the meshes in every direction of the standard FDTD method. By choosing suitable meshes and bandwidth M, our scheme not only retains higher accuracy but also saves memory space and CPU time. Numerical examples are provided to show the high accuracy and effectiveness of proposed scheme.