On Numerical Artifacts of the Complex Envelope ADI-FDTD Method

Abstract

Abstract-We examine two spurious numerical artifacts of the complex envelope (CE) alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method, viz. spurious charges and anomalous wave propagation (modes with positive phase velocity and negative group velocity). These artifacts are also present in the conventional ADI-FDTD; however, the spurious charges in CE-ADI-FDTD have a fundamental distinction from those of ADI-FDTD: they are static in ADI-FDTD and implicitly time-harmonic in CE-ADI-FDTD. Spurious charges are particularly detrimental to CE-ADI-FDTD simulations because they produce secondary radiation. We also show that spurious charges can be reduced by a fixed-point iterative correction in CE-ADI-FDTD.Index Terms-Alternating-direction-implicit finite-difference time-domain (ADI-FDTD), complex envelope (CE), divergence, spurious mode.

FDTD Dispersive Modeling With High-Order Rational Constitutive Parameters

“…Using the numerical permittivity and the complex exponential expression of field vectors [17], [18], we obtain the following numerical dispersion relation…”

A Study on Unconditionally Stable FDTD Methods for the Modeling of Metamaterials

“…The coefficients for are same as those in ADI-FDTD, but, for they are same as those in conventional LOD-FDTD. In terms of coefficients for , they are same as those in conventional LOD-FDTD for the second substep, but, for the first substep they are written as follows (58) We note that the above expression can be derived by using matrix operators as follows [20], [27] (59) (60) (61) where and are same, as in (44) and (45). It should be noted that in this work the equivalent Drude currents , , and are involved at a central time instant when updating corresponding field components.…”

“…7. As shown in this figure, the accuracy of unconditionally stable formalisms gets worse as increases ( decreases), since the splitting and numerical dispersion errors are proportional to [16], [18], [44], [45]. LOD-FDTD has larger relative error than that of the other two (second-order accurate) unconditionally stable formalisms for the modeling of doubly dispersive metamaterials, similarly to the modeling of an air-filled cavity [28].…”

Analysis of Planar Circuits Using an Efficient Laguerre-Based FDTD Method

“…The numerical simulations demonstrate the validity of this Laguerre-based FDTD method. The timedomain and frequencydomain simulation results indicate that, at the comparable accuracy, the efficiency of the proposed method with an iterative procedure is superior to the FDTD method and the alternating-direction implicit (ADI) FDTD method [17][18][19][20].…”