Implicit ID-FDTD algorithm based on Crank-Nicolson scheme: Dispersion relation and stability analysis

Hyun Kim, Il Suek Koh, Jong Gwan Yook

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11 Citations (Scopus)


A new implicit isotropic-dispersion finite difference time domain (ID-FDTD) algorithm is proposed, which is formulated based on the Crank-Nicolson (CN) implicit scheme. The update equation of the new scheme is given for a three dimension (3D) problem and a general lossy medium including electric and magnetic losses. The dispersion relation of the CN ID-FDTD scheme is obtained based on the eigen-analysis technique. Also, the unconditional stability is mathematically proved by using the energy method. For a practical application, a maximum time-limit is proposed for free space. To validate the proposed scheme, a 2D cavity problem is considered. The electric fields inside the cavity, which are calculated by the proposed, conventional CN FDTD schemes, and the exact solution, are compared.

Original languageEnglish
Article number5752237
Pages (from-to)2259-2267
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number6 PART 2
Publication statusPublished - 2011 Jun

Bibliographical note

Funding Information:
Manuscript received May 24, 2010; revised October 13, 2010; accepted November 25, 2010. Date of publication April 19, 2011; date of current version June 02, 2011. This work was supported in part by the LG Yonam Foundation, Korea, and in part by The Ministry of Knowledge Economy (MKE), Korea, under the Information Technology Research Center (ITRC) support program supervised by the National IT Industry Promotion Agency (NIPA) under Grant NIPA-2010-(C1090-1011-0006).

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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