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A review of weakly conditional stable finite‐difference time‐domain method for modeling electromagnetic problems with fine structures
Author(s) -
Chen Juan,
Mai Huanxiao
Publication year - 2018
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.2341
Subject(s) - finite difference time domain method , stability (learning theory) , polygon mesh , computer science , mathematics , boundary value problem , finite difference method , domain (mathematical analysis) , computational electromagnetics , mathematical optimization , algorithm , mathematical analysis , electromagnetic field , geometry , physics , optics , machine learning , quantum mechanics
The finite‐difference time‐domain (FDTD) method has been proven to be an effective tool for simulating varieties of electromagnetic interaction problems. However, because the Courant‐Friedrich‐Levy condition must be satisfied in this method, its maximum time step size is limited by the minimum size of cell used in the computational domain. So, the FDTD method is inefficient to analyze the electromagnetic problem, which has very fine structures. To deal with this problem, the weakly conditional stable (WCS)‐FDTD method is developed. In the WCS‐FDTD method, the confinement of the fine spatial meshes on the time step size is removed by using the hybrid implicit explicit difference in the directions with fine structures. So, this method has much higher computational efficiency than the FDTD method and is extremely useful for the problems that have fine structures in 2 directions. In this paper, the fundamental theory, including the basic formulations, time stability condition, dispersion error, and absorbing boundary condition of the WCS‐FDTD method are presented. Some applications and important developments of this method are provided, and future possibilities of this method are discussed.