期刊
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
卷 57, 期 9, 页码 2675-2682出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAP.2009.2027045
关键词
Exponential evolution operator (EEO); finite-difference time-domain (FDTD); numerical dispersion; split-step scheme; unconditionally stable
资金
- Science Fund of China [U0635004, 60801033]
Three novel finite-difference time-domain (FDTD) methods based on the split-step (SS) scheme with high-order accuracy are presented, which are proven to be unconditionally stable. In the first novel method, symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into six sub-matrices. Accordingly, the time step is divided into six sub-steps. The second and third proposed methods are obtained by adjusting the sequence of the sub-matrices deduced in the first method, so all the novel methods presented in the paper have similar formulations, of which the numerical dispersion errors and the anisotropic errors are lower than the alternating direction implicit finite-difference time-domain (ADI-FDTD) method, the initial SS-FDTD method and the modified SS-FDTD method based on the Strang-splitting scheme. Specifically, for the second method, corresponding to a certain cell per wavelength (CPW), there is a Courant number value making the numerical anisotropic error to be zero, while in the third novel method, corresponding to a certain Courant number value, there exists a CPW making the numerical anisotropic error to be zero. In order to demonstrate the high-order accuracy and efficiency of the proposed methods, numerical results are presented.
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