High-Order Split-Step Unconditionally-Stable FDTD Methods and Numerical Analysis

• Published in: IEEE transactions on antennas and propagation Vol. 59; no. 9; pp. 3280 - 3289
• Main Authors: KONG, Yong-Dan, CHU, Qing-Xin
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Accuracy; Applied classical electromagnetism; Approximation; Coplanar waveguides; Dispersion; Dispersions; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Finite difference method; Finite difference methods; Finite difference time domain method; Finite-difference time-domain (FDTD); Fundamental areas of phenomenology (including applications); high- order; Mathematical analysis; Methods; Nodular iron; numerical dispersion; Operators; Physics; split-step scheme; Studies; Symmetric matrices; Three dimensional; Three dimensional displays; Time domain analysis; unconditionally stable; Performance evaluation; Alternating direction method; Second order; Implicit method; Dispersion relations; numerical dispersion; Digital simulation; high-order; Finite difference time-domain analysis; Numerical method; Maxwell equations; Finite-difference time-domain (FDTD); Three dimensional model; Accuracy; split-step scheme; Differential operator; unconditionally stable; Finite difference method
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2011.2161543

High-order split-step unconditionally-stable finite-difference time-domain (FDTD) methods in three-dimensional (3-D) domains are presented. Symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into four sub-matrices. Accordingly, the time step is divided into four sub-steps. In addition, high-order central finite-difference operators based on the Taylor central finite-difference method are used to approximate the spatial differential operators first, and then the uniform formulation of the proposed high-order schemes is generalized. Subsequently, the analysis shows that all the proposed high-order methods are unconditionally stable. The generalized form of the dispersion relations of the proposed high-order methods is carried out. Moreover, the effects of the mesh size, the time step and the order of schemes on the dispersion are illustrated through numerical results. Specifically, the normalized numerical phase velocity error (NNPVE) and the maximum NNPVE of the proposed second-order scheme are lower than that of the alternating direction implicit (ADI) FDTD method. Furthermore, the analysis of the accuracy of the proposed methods is presented. In order to demonstrate the efficiency of the proposed methods, numerical experiments are presented.