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ADI-FDTD Method for Two-Dimensional Transient Electromagnetic Problems

Part of: Partial differential equations, boundary value problems

Published online by Cambridge University Press:  15 January 2016

Wanshan Li ,
Yile Zhang ,
Yau Shu Wong  and
Dong Liang
Wanshan Li
Affiliation:
School of Mathematics, Shandong University, Jinan 250199, P.R. China
Yile Zhang*
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Yau Shu Wong
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada
Dong Liang
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada
*
*Corresponding author. Email addresses:wanshanli@mail.sdu.edu.cn (W. Li), yile2@ualberta.ca (Y. Zhang), yauwong@ualberta.ca (Y. S. Wong), dliang@mathstat.yorku.ca (D. Liang)
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Abstract

An efficient and accurate numerical scheme is proposed for solving the transverse electric (TE) mode electromagnetic (EM) propagation problem in two-dimensional earth. The scheme is based on the alternating direction finite-difference time-domain (ADI-FDTD) method. Unlike the conventional upward continuation approach for the earth-air interface, an integral formulation for the interface boundary is developed and it is effectively incorporated to the ADI solver. Stability and convergence analysis together with an error estimate are presented. Numerical simulations are carried out to validate the proposed method, and the advantage of the present method over the popular Du-Fort-Frankel scheme is clearly demonstrated. Examples of the electromagnetic field propagation in the ground with anomaly further verify the effectiveness of the proposed scheme.

Keywords

ADI-FDTDinterface boundarystability and convergence analysis

MSC classification

Secondary: 65N06: Finite difference methods 65N12: Stability and convergence of numerical methods 65N15: Error bounds 65N22: Solution of discretized equations
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 1 , January 2016 , pp. 94 - 123
Copyright
Copyright © Global-Science Press 2016 

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