The Research On A FDTD Method With Weakly Conditional Stability And Its Applications Of Microstrip Circuits

The finite-difference time-domain (FDTD) method has been applied in varieties of computationalelectromagnetic fields for its convenience and accuracy. In the real computation on the microwave circuits,the FDTD method has been getting more and more attention for its simplicity and validity. Nevertheless, asan explicit time-stepping scheme, for the problems with fine structure, the computation time of theconventional FDTD method are greatly increased. Recently, to eliminate the Courant-Friedrich-Levy (CFL)constraint on the time step size in conventional FDTD method, some unconditionally stable implicitmethods such as alternating-direction implicit FDTD (ADI-FDTD) method and so on are developed. Butthey also have their own restrictions, for example, they are complex, have lower accuracy in computation,and will result in numerical dispersion errors for larger step size.Based on the advantage of implicit methods, a new method–the hybrid implicit-explicit FDTD(HIE-FDTD) method has been developed. The HIE-FDTD method is between the explicit and implicitformat, keeps a weaker CFL condition, and its time step can be larger than that of conventional FDTDmethod. Meanwhile, the HIE-FDTD method has lower complexities and higher accuracy than theADI-FDTD method and other implicit methods. It can save memory in the case of keeping the sameprecision with conventional FDTD method. The HIE-FDTD method is very useful with problems that needa fine mesh in one direction.This paper is on the research of the HIE-FDTD method. First, the theory is distinguished betweenconventional FDTD method and the ADI-FDTD method. In this paper, the numerical stability of theHIE-FDTD method is demonstrated, and the numerical dispersion characteristics of the HIE-FDTD methodwith cubic and non-cubic mesh are carefully discussed. And the results are also compared withconventional FDTD method and the ADI-FDTD method, then the conclusion is reached that the accuracyof the HIE-FDTD method is better than the ADI-FDTD method, but worse than conventional FDTDmethod.Secondly, the key technologies for implementing the HIE-FDTD method are also introduced andapplied in detail. For the application of the HIE-FDTD method, some microstrip planar circuits areanalyzed. The results of conventional FDTD method and the ADI-FDTD method are also compared.Results analyzed by the HIE-FDTD method agree well with that of conventional FDTD, and the requiredcentral process unit (CPU) time is much less than that of the ADI-FDTD method. It exhibits that the highaccuracy and high efficiency of the HIE-FDTD method. Finally, some improvements about the HIE-FDTD method are rendered. Compact difference schemeis introduced and has been applied in the HIE-FDTD method. Then the propagations of electromagneticwave in waveguide system of lossless and lossy medium with compact HIE-FDTD method are simulated,which proves the high efficiency of the compact HIE-FDTD method.