On the Analytical Solution of the FDTD Method

Wei Fan; Zhizhang Chen; Shunchuan Yang

doi:10.1109/TMTT.2016.2604310

On the Analytical Solution of the FDTD Method

Wei Fan
, Zhizhang Chen
, Shunchuan Yang

Dalhousie University
University of Electronic Science and Technology of China
University of Toronto

科研成果: 期刊稿件 › 文章 › 同行评审

20 引用（Scopus）

摘要

The finite-difference time-domain (FDTD) method is an effective and widely used time-domain method for solving electromagnetic problems. Conventionally, its solutions are obtained numerically in a march-on-in-time manner. In this paper, based on the eigenmatrix theory, we derive the analytical expression for the FDTD solution. The FDTD solution is analytically expressed in terms of spatial modes modulated by discrete time sequences related to the eigenvalues of the FDTD system equation. Based on our results, we propose an alternative approach to the FDTD solutions and it could open a new horizon for applying advanced signal processing techniques as well as offering the possibility of storing the FDTD results in an analytical form for a structure after computation.

源语言	英语
文章编号	7571186
页（从-至）	3370-3379
页数	10
期刊	IEEE Transactions on Microwave Theory and Techniques
卷	64
期	11
DOI	https://doi.org/10.1109/TMTT.2016.2604310
出版状态	已出版 - 11月 2016
已对外发布	是

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title = "On the Analytical Solution of the FDTD Method",

abstract = "The finite-difference time-domain (FDTD) method is an effective and widely used time-domain method for solving electromagnetic problems. Conventionally, its solutions are obtained numerically in a march-on-in-time manner. In this paper, based on the eigenmatrix theory, we derive the analytical expression for the FDTD solution. The FDTD solution is analytically expressed in terms of spatial modes modulated by discrete time sequences related to the eigenvalues of the FDTD system equation. Based on our results, we propose an alternative approach to the FDTD solutions and it could open a new horizon for applying advanced signal processing techniques as well as offering the possibility of storing the FDTD results in an analytical form for a structure after computation.",

keywords = "Analytical solution, Courant-Friedrichs-Lewy (CFL), eigendecomposition, finite difference time domain (FDTD), numerical stability, spatial modes",

author = "Wei Fan and Zhizhang Chen and Shunchuan Yang",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.",

year = "2016",

month = nov,

doi = "10.1109/TMTT.2016.2604310",

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T1 - On the Analytical Solution of the FDTD Method

AU - Fan, Wei

AU - Chen, Zhizhang

AU - Yang, Shunchuan

PY - 2016/11

Y1 - 2016/11

N2 - The finite-difference time-domain (FDTD) method is an effective and widely used time-domain method for solving electromagnetic problems. Conventionally, its solutions are obtained numerically in a march-on-in-time manner. In this paper, based on the eigenmatrix theory, we derive the analytical expression for the FDTD solution. The FDTD solution is analytically expressed in terms of spatial modes modulated by discrete time sequences related to the eigenvalues of the FDTD system equation. Based on our results, we propose an alternative approach to the FDTD solutions and it could open a new horizon for applying advanced signal processing techniques as well as offering the possibility of storing the FDTD results in an analytical form for a structure after computation.

AB - The finite-difference time-domain (FDTD) method is an effective and widely used time-domain method for solving electromagnetic problems. Conventionally, its solutions are obtained numerically in a march-on-in-time manner. In this paper, based on the eigenmatrix theory, we derive the analytical expression for the FDTD solution. The FDTD solution is analytically expressed in terms of spatial modes modulated by discrete time sequences related to the eigenvalues of the FDTD system equation. Based on our results, we propose an alternative approach to the FDTD solutions and it could open a new horizon for applying advanced signal processing techniques as well as offering the possibility of storing the FDTD results in an analytical form for a structure after computation.

KW - Analytical solution

KW - Courant-Friedrichs-Lewy (CFL)

KW - eigendecomposition

KW - finite difference time domain (FDTD)

KW - numerical stability

KW - spatial modes

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DO - 10.1109/TMTT.2016.2604310

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AN - SCOPUS:84988566093

SN - 0018-9480

VL - 64

SP - 3370

EP - 3379

JO - IEEE Transactions on Microwave Theory and Techniques

JF - IEEE Transactions on Microwave Theory and Techniques

IS - 11

M1 - 7571186

ER -

On the Analytical Solution of the FDTD Method

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