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

The Korean Institute of Electromagnetic Engineering and Science (한국전자파학회)
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2D Crank-Nicolson FDTD Method Based on Isotropic-Dispersion Finite Difference Equation for Lossy Media

손실 매질에 대한 Isotropic-Dispersion 유한 차분식의 2D Crank-Nicolson FDTD 기법

  • Kim, Hyun (Dept. of Electrical and Electronics Engineering, Yonsei University) ;
  • Koh, Il-Suek (Graduate School of Information and Communication, Inha University) ;
  • Yook, Jong-Gwan (Dept. of Electrical and Electronics Engineering, Yonsei University)
  • 김현 (연세대학교 전기전자공학과) ;
  • 고일석 (인하대학교 정보통신대학원) ;
  • 육종관 (연세대학교 전기전자공학과)
  • Accepted : 2010.06.23
  • Published : 2010.07.31
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Abstract

The Crank-Nicolson isotropic-dispersion finite difference time domain(CN ID-FDTD) scheme is proposed based on isotropic-dispersion finite difference(ID-FD) $equation^{[1],[2]}$. The dispersion relation of CN ID-FDTD is derived for lossy media by solving the eigenvalue problem of iteration matrix in spatial spectral domain, in addition, the weighting factors and scaling factors of the CN ID-FDTD scheme are presented for low dispersion error. The CN ID-FDTD scheme makes the dispersion error drastically reduced and shows accurate numerical results compared to the conventional Crank-Nicolson FDTD method.

기존 Crank-Nicolson FDTD 기법(CN FDTD 기법)의 비등방성 분산 특성을 개선하기 위한 CN ID-FDTD 기법을 제안하였다. 제안한 CN ID-FDTD 기법은 공간 미분 연산을 위해 기존 CN FDTD 기법의 centered 유한 차분식 (Finite Difference equation: FD 연산식)이 아닌 isotropic-dispersion 유한 차분식(ID-FD 연산식)$^{[1],[2]}$을 이용한다. 본 논문에서는 손실 매질에 대한 CN ID-FDTD 기법의 분산 관계식을 유도하였고, 이 분산 관계식을 이용해 ID-FD 연산식에서 분산 오차(dispersion error)를 줄이는 가중치(weighting factor)와 보정값(scaling factor)을 제시하였다. 그리고 해석 결과의 정확성 비교를 통해 CN ID-FDTD 기법에서는 기존 CN FDTD 기법의 단점이었던 비등방성 분산 오차가 확연하게 감소하는 것을 확인하였다.

Keywords

References

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