A New Efficient Algorithm for the Unconditionally Stable 2-D WLP-FDTD Method

We previously introduced an efficient algorithm for implementing the 2-D Laguerre-based finite-difference time-domain (FDTD) method. Numerical results indicated that the efficient algorithm can save CPU time and memory storage greatly while maintaining comparable computational accuracy. However, the splitting error associated with the perturbation term becomes pronounced in regions with larger spatial derivatives of the field. In this paper, we present a new efficient algorithm based on the use of an iterative procedure to reduce the splitting error. The new algorithm does not involve any nonphysical intermediate variables, and its update equations are much simpler and more concise than the original ones. Instead of applying the iterative procedure uniformly to the entire computational domain, one can apply an additional number of iterations to regions with relatively large field variation. Using this approach, the overall accuracy can be improved with little computational overhead. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.