Study Of Some Key Problems Of The Finite-Difference Time-Domain Method And Its Applications

Some key problems of the finite-difference time-domain method (FDTD) with the emphasis on absorbing boundary conditions (ABCs) are studied in this paper and some practical electromagnetic problems are analyzed with FDTD.A generalized ABC is acquired on the basis of pseudo-differential operator of one-way wave, and the differential equation for Liao抯 ABC is presented as the steplengths approach zero as a limit. The study of the consistency of ABCs shows that Higdon抯 operator, Mur抯 ABC, dispersive ABC and etc. can be regarded as special cases of the generalized ABC. The optimization of the coefficients of the generalized ABC is discussed under two norms which include the norm of the minimum for average reflection at the range of entire incidence angle and the equi-ripple norm within the given range of incidence angle. The influence of different difference approximations to the absorbing performance and the stability of the generalized ABC is analyzed according to second order Mur抯 ABC.Numerical dispersion characteristic and impedance relationship of three dimensional perfectly matched layers (PML) are analyzed under finite difference approximation in this paper, respectively, which show that numerical dispersion relationship of PML is different from that of the FDTD equations and the impedance of homogeneous PML medium is the same as that of free space. The absorbing performance of one dimensional PML is theoretically analyzed and numerically simulated in view of the error caused by finite difference approximation, respectively, whose results show that this theoretical analysis can exactly indicate practical circumstances. The analyses above are applicable to any lossy medium layers among which PML is only one case. Considering the difference error in the region where the conductivity is acutely varied, which mostly confines the absorbing performance of PML, the concept of numerically matched condition is proposed and PML is divided into numerically matched region and analytically matched region, which can widely improve the absorbing performance of PML and reduce computation expense. This idea is extended to three dimensional PML. A lossy ABC is proposed to truncate computation region of PML, and two finite difference equations are presented including the space exponential finite difference equation and the time exponential finite difference equation. Then, the influence of outer boundary conditions and conductivity profiles of PML to its absorbing performance is synthetically discussed.A restrictive condition with which the width of Gaussian pulse signal in time domain and in frequency domain must be satisfied, respectively, is presented to reduce numericaldispersion error and to satisf~j initial value condition and to utilize as much the energy of the signal as possible. A stable resistance-free current-fed model and a stable resistive currentfed model are proposed respectively. The former is simple in implementation and high in computation accuracy, but it is unsuitable for the analysis of electromagnetic problems in which there exists nearly lossless in certain frequencies. The latter does not cause any instability of the algorithm as the resistance rises, contrarily, computation time is reduced as the resistance suitably rises by comparison with the resistive voltage-fed model.Signal extraction techniques in combination with the finite-difference time-domain method are studied to analyze electromagnetic problems which have uniform transmission line structures. A signal extraction technique in frequency domain and one in time domain are proposed, respectively, among which the former is applicable to the analysis of lossy and dispersive transmission lines and the latter is only applicable to the analysis of nondispersive ones, however, computation accuracy of the former is lower than that of the latter. Because only one time-domain simulation is required using those techniques, computation time can be reduced by comparison with traditional method.Finally, some k...