A hybrid implicit‐explicit FDTD scheme with weakly conditional stability

Abstract

ϭ 3 ϫ 10 7 S/m, and the input modulated Gaussian pulse is V 0 ϭ 1.0 V, ϭ 16.68 ps, and t 0 ϭ 66.68 ps.As in Figure 4, the attenuation of the propagating sinusoidally modulated Gaussian pulse is due mainly to the ohmic loss of both the center strip and ground planes. Also, the attenuation is more rapid at the start of the pulse propagation distance. CONCLUSIONSBased on an improved empirical formula to calculate the ohmic loss of CPWs, the lossy effects in coplanar waveguides on the pulse propagation have been studied. These CPWs are assumed to be fabricated on single-layer, low-dispersion and low-loss LTCC. For normal LTCC CPWs, it is shown that the total loss is contributed mainly by the ohmic loss of the conductive planes in the frequency range up to 40 GHz. The ohmic loss can lead to nearly 50% pulse magnitude attenuation at the start of the propagation distance of less than several millimeters.

A Hybrid Implicit-Explicit Spectral FDTD Scheme for Oblique Incidence Problems on Periodic Structures

“…In the HIE technique [29,30], E x and H x fields are defined at time steps n − 1/2 and n + 1/2, and other fields components are defined at time steps n and n + 1. For E x and H x components, we use the explicit-difference technique at integer time step n, whereas for other components, we use semi-implicit difference technique at time step n + 1/2.…”

“…For E x and H x components, we use the explicit-difference technique at integer time step n, whereas for other components, we use semi-implicit difference technique at time step n + 1/2. By applying the HIE technique [29,30] to (2) and (3), Maxwell's equations can be written in a matrix form as,…”

“…Meanwhile, in the ADI-SFDTD method, four untridiagonal matrices, two tridiagonal matrices, and six explicit equations should be solved in one update cycle, which makes it computationally inefficient. To overcome the drawbacks of the ADI-FDTD, recently, a hybrid implicit-explicit (HIE) FDTD method was submitted [29,30], the computation complexity of the HIE-FDTD method is the same as that of the conventional FDTD method, while the CFL condition restraint is weaker than that of the conventional FDTD method and consequently, less CPU time is required. This advantage can be more obvious when fine structures are involved.…”

A Novel 3-D Weakly Conditionally Stable FDTD Algorithm

“…By adopting the proposed technology, the field advancement only needs to solve four implicit equations, and the time step size will no longer be bounded by the fine grid cell sizes, which is only determined by the large space discretisation. Numerical stability analysis demonstrates that the CFL stability condition of the proposed algorithm is more relaxed than those of the existing WCS-FDTD methods [19,20], which means the proposed method is more efficient due to the larger time step size can be chose. Compared with the ADI-FDTD scheme, the numerical phase velocity error of the proposed algorithm is reduced, especially for large time-step size.…”

“…In practice, some electromagnetic structures, such as patch antennas and shielding enclosure with thin slots, only have fine structures in one or two directions where fine grids are needed. For investigating the electromagnetic performances of those structures, some WCS-FDTD methods have been presented [19,20].…”