The Journal of Korean Institute of Electromagnetic Engineering and Science (한국전자파학회논문지)

The Korean Institute of Electromagnetic Engineering and Science (한국전자파학회)
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Transient Analysis of General Dispersive Media Using Laguerre Functions

라게르 함수를 이용한 일반적인 분산 매질의 시간 영역 해석

  • Lee, Chang-Hwa (School of Electronic Engineering, Kyungpoon National University) ;
  • Kwon, Woo-Hyen (School of Electronic Engineering, Kyungpoon National University) ;
  • Jung, Baek-Ho (Dept. of Information and Communication Engineering, Hoseo University)
  • Published : 2011.10.31
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Abstract

In this paper, we present a marching-on-in-degree(MOD) finite difference method(FDM) based on the Helmholtz wave equation for analyzing transient electromagnetic responses in a general dispersive media. The two issues related to the finite difference approximation of the time derivatives and the time consuming convolution operations are handled analytically using the properties of the Laguerre functions. The basic idea here is that we fit the transient nature of the fields, the flux densities, the permittivity with a finite sum of orthogonal Laguerre functions. Through this novel approach, not only the time variable can be decoupled analytically from the temporal variations but also the final computational form of the equations is transformed from finite difference time-domain(FDTD) to a finite difference formulation through a Galerkin testing. Representative numerical examples are presented for transient wave propagation in general Debye, Drude, and Lorentz dispersive medium.

본 논문에서는 일반적인 분산 매질의 전자기 과도 응답을 해석하기 위하여 헬름홀츠 방정식에 근거한 MODFDM(Marching-on-in-Degree Finite Difference Method) 기법을 제안한다. 라게르 함수의 특성을 이용하여 시간에 대한 미분항과 상승 적분(convolution integral)의 근사를 해석적으로 처리하였다. 본 기법의 기본적인 독창성은 전장과 전속 밀도, 유전율 등을 모두 라게르 함수로 전개한 다음, 갤러킨 시험 과정을 적용하여 시간 변수를 완전히 제거하였을 뿐만 아니라, 기존의 FDTD(Finite Difference Time-Domain) 방법과 달리 최종 계산식에 공간적인 유한 차분만을 적용하는데 있다. 일반적인 분산 매질의 해석에 적용 가능함을 보이기 위하여 대표적인 드바이, 드루드 및 로렌츠 분산 매질에 대한 전자기 과도 응답을 수치예로 보인다.

Keywords

References

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