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PIER PIER B PIER C PIER M PIER Letters
2013-01-10
High-Order Unconditionally-Stable Four-Step Adi-FDTD Methods and Numerical Analysis
By
Yong-Dan Kong,

    Dr. Yong-Dan Kong

    School of Electronic and Information Engineering

    South China University of Technology

    China

    Homepage

Qing-Xin Chu,

    Prof. Qing-Xin Chu

    School of Electronic and Information Engineering

    South China University of Technology

    China

    Homepage

Rong-Lin Li

    Prof. Rong-Lin Li

    Georgia Institute of Techonology

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 135, 713-734, 2013
doi:10.2528/PIER12102205
Abstract
High-order unconditionally-stable three-dimensional (3-D) four-step alternating direction implicit finite-difference time-domain (ADI-FDTD) methods are presented. Based on the exponential evolution operator (EEO), the Maxwell's equations in a matrix form can be split into four sub-procedures. 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. Finally, in order to demonstrate the validity of the proposed methods, numerical experiments are presented. Furthermore, the effects of the order of schemes, the propagation angle, the time step, and the mesh size on the dispersion are illustrated through numerical results. Specifically, the normalized numerical phase velocity error (NNPVE) and the maximum NNPVE of the proposed schemes are lower than that of the traditional ADI-FDTD method.
Citation
Yong-Dan Kong, Qing-Xin Chu, and Rong-Lin Li, "High-Order Unconditionally-Stable Four-Step Adi-FDTD Methods and Numerical Analysis," Progress In Electromagnetics Research, Vol. 135, 713-734, 2013.
doi:10.2528/PIER12102205
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