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A Crank–Nicholson‐based unconditionally stable time‐domain algorithm for 2D and 3D problems
Author(s) -
Xie Xin,
Pan George,
Hall Stephen
Publication year - 2007
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.22101
Subject(s) - finite difference time domain method , limit (mathematics) , stability (learning theory) , benchmark (surveying) , mathematics , algorithm , time domain , truncation (statistics) , computer science , mathematical analysis , physics , quantum mechanics , statistics , geodesy , machine learning , computer vision , geography
It has been shown that both ADI‐FDTD and CN‐FDTD are unconditionally stable. While the ADI is a second‐order approximation, CN is only in the first order. However, analytical expressions reveal that the CN‐FDTD has much smaller truncation errors and is more accurate than the ADI‐FDTD. Nonetheless, it is more difficult to implement the CN than the ADI, especially for 3D problems. In this paper, we present an unconditionally stable time‐domain method, CNRG‐TD, which is based upon the Crank–Nicholson scheme and implemented with the Ritz–Galerkin procedure. We provide a physically meaningful stability proof, without resorting to tedious symbolic derivations. Numerical examples of the new method demonstrate high precision and high efficiency. In a 2D capacitance problem, we have enlarged the time step, Δt, 400 times of the CFL limit, yet preserved good accuracy. In the 3D antenna case, we use the time step, Δt, 7.6 times larger that that of the ADI‐FDTD i.e., more than 38 times of the CFL limit, with excellent agreement of the benchmark solution. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 261–265, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22101