A Novel 3-D HIE-FDTD Method With One-Step Leapfrog Scheme

• Published in: IEEE transactions on microwave theory and techniques Vol. 62; no. 6; pp. 1275 - 1283
• Main Authors: Wang, Jianbao, Zhou, Bihua, Shi, Lihua, Gao, Cheng, Chen, Bin
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Courant-Friedrich-Levy (CFL) stability condition; Dispersion; Dispersions; Equations; Exact sciences and technology; Finite difference method; Finite difference methods; hybrid implicit-explicit finite-difference time-domain (HIE-FDTD); Implicit methods; Mathematical analysis; Mathematical models; Mathematics; Microwaves; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; numerical dispersion relation; Numerical stability; one-step leapfrog scheme; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Power system stability; Sciences and techniques of general use; Stability analysis; Three dimensional; Time-domain analysis; Alternating direction method; Stability; Dispersion relation; Grid; Modeling; Partial differential equation; Wave dispersion; Leap frog configuration; Time domain method; Courant-Friedrich-Levy (CFL) stability condition; one-step leapfrog scheme; hybrid implicit-explicit finite-difference time-domain (HIE-FDTD); numerical dispersion relation; Auxiliary variable; Numerical convergence; Finite difference method
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2014.2320692

This paper presents a novel 3-D leapfrog hybrid implicit-explicit finite-difference time-domain (HIE-FDTD) method. By first adopting the Peaceman-Rachford scheme and then the one-step leapfrog scheme, the proposed HIE-FDTD algorithm is implemented in the same manner as the traditional finite-difference time-domain method in which the implicit scheme was applied only in the direction where a fine grid was applied and the explicit scheme was applied in two other directions where a larger grid was used. Further, by introducing auxiliary field variables denoted by e and h, the proposed algorithm is reformulated in a much simpler form with more concise right-hand sides for an efficient implementation. Numerical analysis demonstrated that the Courant-Friedrichs-Lewy stability condition of the proposed HIE-FDTD method is determined only by one grid cell size, which is more relaxed than those of the existing HIE-FDTD methods, and the numerical dispersion error is less than that of the alternating-direction implicit method.