Abstract
To obtain high accuracy and efficiency in the simulations, an optimum time step should be taken in finite-difference time-domain (FDTD) methods. The authors investigated how time steps impact on numerical dispersion of two FDTD methods including the FDTD(2,2) method and the FDTD(2,4) method. Through rigorously analytical and numerical analysis, it is found that small time steps of the FDTD methods do not always have small numerical errors. Our findings reveal that these two FDTD methods present different behaviours with respect to time steps: (1) for the FDTD(2,2) method, smaller time steps limited by the Courant-Friedrichs-Lewy condition increase numerical dispersion and lead to larger simulation errors and (2) for the FDTD(2,4) method, as the time step increases, numerical dispersion errors first decrease and then increase. Our findings are also comprehensively validated from one- to three-dimensional cases through several numerical examples including wave propagation, resonant frequencies of cavities and a practical engineering problem.
Highlights
INTRODUCTIONT HE finite-difference time-domain (FDTD) method is one of the most widely used numerical methods to solve the practical electromagnetic problems, like scattering from electrically large and multiscale objects [1]–[3], integrated circuits [4]–[7], electromagnetic compatibility (EMC) [8]–[10], electromagnetic interference (EMI) [11]–[13], due to its easy implementation, robustness, strong capability of handling complex media and highly efficient parallel computation [14], [15]
A wave propagation example is used to verify the accuracy of the two finite-difference time-domain (FDTD) methods with different time steps in one dimensional case
In this paper, we comprehensively investigated how time steps affect the accuracy of the FDTD methods in terms of numerical dispersion
Summary
T HE finite-difference time-domain (FDTD) method is one of the most widely used numerical methods to solve the practical electromagnetic problems, like scattering from electrically large and multiscale objects [1]–[3], integrated circuits [4]–[7], electromagnetic compatibility (EMC) [8]–[10], electromagnetic interference (EMI) [11]–[13], due to its easy implementation, robustness, strong capability of handling complex media and highly efficient parallel computation [14], [15]. The accuracy of the FDTD methods can be affected by several factors, such as numerical dispersion, mesh size, staircase errors, time steps, and so on. One simple but suboptimal option is to use fine enough grid in the FDTD simulations It increases the accuracy [30], inevitably with significantly increasing computational resources in terms of memory and CPU time since quite small mesh has to be used to capture fine geometric features, like wires and slots. Numerical dispersion can severely degenerate the accuracy and even totally unacceptable It implies that long simulation time has been inevitable because of small time steps used in the FDTD methods.
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