A Leapfrog Scheme for Complying-Divergence Implicit Finite-Difference Time-Domain Method

• Published in: IEEE antennas and wireless propagation letters Vol. 20; no. 5; pp. 853 - 857
• Main Author: Tan, Eng Leong
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Alternating direction implicit (ADI); computational electromagnetics; Differential operators; Divergence; Eigenvalues; Eigenvalues and eigenfunctions; Finite difference methods; Finite difference time domain method; finite-difference time-domain (FDTD) method; Floating point arithmetic; implicit scheme; leapfrog scheme; Mathematical analysis; Numerical stability; Permittivity; Stability analysis; Stability criteria; Time domain analysis; unconditionally stable method
• ISSN: 1536-1225; 1548-5757
• DOI: 10.1109/LAWP.2021.3065520

A leapfrog scheme for the unconditionally stable complying-divergence implicit (CDI) finite-difference time-domain (FDTD) method is presented. The leapfrog CDI-FDTD method is formulated to comprise distinctive implicit and explicit update procedures. The implicit update procedures are in the fundamental form with operator-free right-hand sides (RHS), whereas the explicit ones are compatible and correspond to the familiar explicit FDTD method. Using the Fourier (von Neumann) approach, the stability of the leapfrog CDI-FDTD method is analyzed. The eigenvalues of amplification matrix are obtained to prove the unconditional stability. Furthermore, the leapfrog alternating direction implicit (ADI) FDTD and CDI-FDTD methods are discussed and compared, including the RHS floating-point operations (flops) count, for-loops and memory. The leapfrog CDI-FDTD requires merely half the flops of leapfrog ADI-FDTD at RHS while retaining the same left-hand sides (LHS) of implicit update equations and the same number of for-loops without much extra memory. Discussions and numerical results are presented to demonstrate the advantages of leapfrog CDI-FDTD method including unconditional stability, complying divergence, and efficient leapfrog scheme with reduced RHS flops.