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This letter introduces an unconditionally stable finite‐difference time‐domain (FDTD) method, based on the locally one‐dimensional (LOD) technique, for the solution of the two‐dimensional scalar wave equation (WE) in homogeneous media. The second spatial derivatives in the WE are discretized by using a three‐point compact (implicit) finite‐difference formula with a free parameter. This formula has second‐order accuracy and becomes fourth‐order by properly selecting the parameter value. Moreover, the resulting algorithm only involves tridiagonal matrices, as when using standard (explicit) second‐order finite differences. Additionally, a stability analysis is performed and the numerical dispersion relation of the method is derived. The proposed compact LOD‐WE‐FDTD technique has been applied to the calculation of resonant frequencies in a metallic ridge cavity. The accuracy of the results obtained has been studied as a function of the parameter value. [ABSTRACT FROM AUTHOR]

While the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method preserves the second-order temporal accuracy of the conventional FDTD technique, the locally one-dimensional (LOD)-FDTD method exhibits a first-order in time splitting error. Despite this difference, the numerical dispersion analyses of these methods reveal that both present similar accuracy properties. For this reason, the characteristic noncommutativity error of the LOD-FDTD scheme has not received much attention. In this letter, we determine the closed form of the local truncation error for the 3D-LOD-FDTD scheme. We find that it presents error terms that depend on the time-step size multiplied by the spatial derivatives of the fields. Numerical results confirm that these terms become a significant source of error that is not revealed in the dispersion analyses. [ABSTRACT FROM AUTHOR]

In recent years, split-step finite-difference time-domain (SS-FDTD) methods have attracted much attention and many implementations have been developed to improve their accuracy and efficiency. In this communication the equivalence between some of these recently reported techniques and conventional schemes is shown. More specifically, we prove that there are four-stage split-step (4SS)-FDTD algorithms that can be reinterpreted as classic two-stage split-step (2SS)-FDTD schemes yielding the same local truncation errors and numerical dispersion relationships. The analytical results are validated by numerical simulations. [ABSTRACT FROM PUBLISHER]

The lumped-network finite-difference time-domain (LN-FDTD) technique is an extension of the conventional FDTD method that enables the incorporation of linear one-port LNs in a single FDTD cell. This paper studies the stability and the numerical dispersion of this technique. To this end, an isotropic medium that is uniformly loaded with LNs in the x-direction is considered as a working model. The stability analysis, based on the von Neumann method, is performed for general Mth-order LNs and closed-form stability conditions are derived for some particular cases. The numerical dispersion relation is obtained for plane-wave propagation in the proposed LN-loaded medium. It is shown that LNs can be interpreted in terms of an effective frequency-dependent permittivity and, as a consequence, the LN-loaded medium can be viewed as a uniaxial medium. The numerical admittance of the LNs is also obtained showing that, as a side-effect of the time discretization, the LN parameters become frequency-dependent, e.g. for the resistor case, the resistance becomes a function of the frequency. [ABSTRACT FROM AUTHOR]

A numerical dispersion analysis of the alternating-direction implicit finite-difference time-domain method for transverse-electric waves in lossy materials is presented. Two different finite-difference approximations for the conduction terms are considered: the double-average and the synchronized schemes. The numerical dispersion relation is derived in a closed form and validated through numerical simulations. This study shows that, despite its popularity, the accuracy of the double-average scheme is sensitive to how well the relaxation-time constant of the material is resolved by the time step. Poor resolutions lead to unacceptably large numerical errors. On the other hand, for good conductors, the synchronized scheme allows stability factors as large as 100 to be used without deteriorating the accuracy significantly. [ABSTRACT FROM AUTHOR]

This paper studies the stability and numerical dispersion of an extension of the original finite-difference time-domain (FDTD) method to incorporate magnetized ferrites. This extension is based on discretizing the ferrite equations by means of central differences and averages. Both partially magnetized and saturated ferrites are considered. With the aim of studying the numerical features of the resulting FDTD algorithms, we have considered the propagation of plane-waves along longitudinally magnetized ferrite materials. This is a simple 1D problem that enables the numerical properties of the algorithms to be studied analytically. A von Neumann stability analysis shows that the stability condition of the original FDTD method is preserved and that the algorithms do not exhibit numerical dissipation. The accuracy of the numerical results is not deteriorated with respect to those obtained in the demagnetized case. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces an extension of the original finite-difference time-domain (FDTD) method for modeling double-negative media characterized by high-order frequency-dependent permittivity and permeability. The approach basically consists of adding electric and magnetic current densities to Maxwell's curl equations and considering Ohm's law as a constitutive relationship. Current densities are discretized by using a weighted average in time and Ohm's law by applying the Mobius transformation technique. The extended FDTD formulation is validated and its numerical features are carefully examined. More specifically, analytical stability conditions are derived for several types of double-negative media and the numerical dissipation issue is discussed. In addition, the numerical dispersion equation for general high-order double-negative media is given and the order of accuracy of the scheme is studied. Finally, the definition of numerical refractive index is addressed and it is shown that, when the discretization parameters of the problem are not properly chosen, a negative refractive index may become a positive one in the discrete world, thus changing the physics of the problem. [ABSTRACT FROM AUTHOR]