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

• Published in: IEEE transactions on antennas and propagation Vol. 61; no. 7; pp. 3712 - 3720
• Main Authors: Chen, Zheng, Duan, Yan-Tao, Zhang, Ye-Rong, Yi, Yun
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Algorithms; Equations; Exact sciences and technology; Finite difference methods; Finite-difference time-domain (FDTD) method; iterative method; Iterative methods; Laguerre polynomials; Mathematical model; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Sciences and techniques of general use; Sparse matrices; Studies; Time-domain analysis; unconditionally stable methods; Iterative method; Laguerre polynomial; Modeling; Finite-difference time-domain (FDTD) method; unconditionally stable methods; Time domain method; Model matching; Laguerre polynomials; Efficiency; Derivative; Numerical stability; Central unit; Finite difference method
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2013.2255093

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.