Stability and dispersion analysis of ADI-MRTD and ADI high-order schemes

M. K. Sun; Wai Yip Tam

doi:10.1002/mop.20717

Stability and dispersion analysis of ADI-MRTD and ADI high-order schemes

M. K. Sun, Wai Yip Tam

The Hong Kong Polytechnic University

Research output: Journal article publication › Journal article › Academic research › peer-review

5 Citations (Scopus)

Abstract

The maximum time-step size of the alternating-direction implicit finite-differenc̀e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.

Original language	English
Pages (from-to)	43-46
Number of pages	4
Journal	Microwave and Optical Technology Letters
Volume	45
Issue number	1
DOIs	https://doi.org/10.1002/mop.20717
Publication status	Published - 5 Apr 2005

Keywords

ADI FDTD method
Battle-Lemarie scaling functions
High-order centered finite difference
Numerical dispersion

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Condensed Matter Physics
Electrical and Electronic Engineering

More information

10.1002/mop.20717

Cite this

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abstract = "The maximum time-step size of the alternating-direction implicit finite-differen{\`c}e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.",

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AU - Tam, Wai Yip

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N2 - The maximum time-step size of the alternating-direction implicit finite-differenc̀e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.

AB - The maximum time-step size of the alternating-direction implicit finite-differenc̀e time-domain (ADI-FDTD) method is not limited by the Courant-Friedrich-Levy (CFL) stability condition. However, the numerical-dispersion error of the ADI-FDTD method is much greater than that of Yee's FDTD method. In this paper, the numerical dispersion is improved by approximating the spatial derivatives using cubic spline Battle-Lemarie scaling functions and the high-order centered differences. The stability condition and the numerical-dispersion relations are derived using the Fourier series method and validated by a numerical simulation. The new scheme is unconditionally stable and the numerical dispersion error can be reduced to the limit of the conventional ADI-FDTD method with the 6th-order centered difference.

KW - ADI FDTD method

KW - Battle-Lemarie scaling functions

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KW - Numerical dispersion

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DO - 10.1002/mop.20717

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JO - Microwave and Optical Technology Letters

JF - Microwave and Optical Technology Letters

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Stability and dispersion analysis of ADI-MRTD and ADI high-order schemes

Abstract

Keywords

ASJC Scopus subject areas

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