On the Analytical Solution of the FDTD Method

被引：14

作者：

Fan, Wei ^{[1
]}

Chen, Zhizhang ^{[1
,2
]}

Yang, Shunchuan ^{[1
,3
]}

机构：

[1] Dalhousie Univ, Dept Elect & Comp Engn, Halifax, NS B3H 4R2, Canada

[2] Univ Elect Sci & Technol China, Chengdu 610051, Peoples R China

[3] Univ Toronto, Dept Elect & Comp Engn, Toronto, ON M5S, Canada

来源：

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES | 2016年 / 64卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Analytical solution; Courant-Friedrichs-Lewy (CFL); eigendecomposition; finite difference time domain (FDTD); numerical stability; spatial modes; DIFFERENCE TIME-DOMAIN; FINITE-DIFFERENCE; EQUATIONS;

D O I：

10.1109/TMTT.2016.2604310

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

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.

引用

页码：3370 / 3379

页数：10

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