Unconditionally-stable Finite-difference Time-domain Research Articles

Crosstalk analysis of dielectric inserted side contact multilayer graphene nanoribbon interconnects for ternary logic system using unconditionally stable FDTD model

In the present work, for examining the performance of dielectric inserted side contact multilayer graphene nano ribbon (DSMLGNR), a novel Unconditionally Stable Finite-Difference Time-Domain (USFDTD) technique is proposed. This technique overcomes the constraint of courant stability condition prevailing in FDTD technique. The proposed mathematical model is highly time efficient and accurately analyzes the crosstalk effects induced among the coupled interconnect lines. The robustness of the USFDTD technique is verified by determining various performance metrics and justifying it with FDTD technique and HSPICE simulations. The obtained results are in accordance with HSPICE and the average percentage error is less than 1%. For performing the transient analysis, USFDTD model consumes 25% lesser time compared to FDTD technique. Furthermore, accuracy of the proposed model is validated by using Feature Selective Validation (FSV) tool.

Hybrid FDTD algorithm for electromagnetic analysis of fine structures

A new hybrid Finite-Difference Time-Domain (hybrid FDTD) algorithm is proposed in this paper. This hybrid FDTD method combines the superiorities of explicit unconditionally stable FDTD (US-FDTD) and traditional FDTD methods to achieve unconditional stability and high calculation efficiency. US-FDTD is used in fine grids and the adjacent coarse grids subdomain and it breaks the Courant-Friedrich-Levy (CFL) condition. Traditional FDTD is used in the remaining coarse grids subdomain and it is a matrix free method. A compensation scheme is used on the subdomain boundary without compromising accuracy. Hybrid FDTD makes the explicit time marching with a uniform time step determined by the size of coarse grid in whole domain, which reduces the iteration time. In addition, because US-FDTD is only used in one of the subdomains, compared with global US-FDTD method, the matrix dimension of hybrid FDTD is reduced, which saves the time for eigenvalue solution. Numerical results show high efficiency and accuracy of the proposed method.

A prominent unified crosstalk model for linear and sub-threshold regions in mixed CNT bundle interconnects

With the feasibility to scale the devices and interconnects in highly sophisticated VLSI technology, the demand for high-speed and low-power e-applications have also subsequently increased stupendously. Based on the applications and requirements, a VLSI system is operated in different modes as linear or sub-threshold. A unified analytical model for describing both these linear and sub-threshold modes is highly desirable. This has been innovatively presented in the current paper. Moreover, the futuristic and emerging mixed carbon nanotube bundle (MCB) as interconnects for both linear and sub-threshold region of operations has been considered. The essential signal integrity analysis comprising of several crosstalk effects such as associated transient response, delay and power have been analyzed. To evaluate this, analytical model is formulated and proposed using accurate unconditionally-stable finite-difference time-domain (USFDTD) technique. Utilizing the proposed model, it is investigated that linear mode of operation is good for realizing high-speed systems while sub-threshold is a preferable operation for applications targeted for low-power. Comprehensively, it is envisaged that the average power-delay-product in MCB interconnects operating in sub-threshold region is low and reduced by 74% compared to corresponding linear region of operation. Also, it is demonstrated that the proposed unified USFDTD based model for MCB interconnects operating in different modes of operation is stable and not constricted by the Courant condition. At maximum allowable time step, the proposed model is nearly 10 and 25 times faster than the conventional FDTD analytical and HSPICE simulation models, respectively. The results reveal that USFDTD technique provides better accuracy than the FDTD technique. The different performance analyses are performed at 22 nm technology node.

Combining standard with optimised split‐step finite‐difference time‐domain methods for the study of graphene configurations

In this study, the authors propose a hybrid computational model for the reliable simulation of electromagnetic-wave phenomena emerging in graphene structures, which incorporates two variations of an unconditionally-stable finite-difference time-domain algorithm. The new approach features: (a) a dispersive model that relies on the auxiliary differential equation technique and takes into consideration the graphene's surface conductivity, and (b) a modified discretisation algorithm implementing error-optimised spatial approximations, which is appropriate for graphene-free mesh nodes. The resulting update equations are devoid of time-step restrictions, thus formulating a suitable and useful computational framework for the investigation of contemporary graphene-based problems, which commonly call for densely-sampled grids and/or prolonged simulations. After theoretically assessing the fundamental features of the proposed algorithm, the propagation properties of surface waves on graphene are extracted numerically and compared with analytical estimations, so that computational validation is provided. In addition, a realistic surface-wave coupler configuration is simulated and its main characteristics are extracted accurately, exemplifying the method's robustness on more complex setups.

New hybrid FDTD algorithm for electromagnetic problem analysis**Project supported by the National Natural Science Foundation of China (Grant No. 61571348) and the Equipment Pre-Research Foundation of China (Grant No. 61405180202).

Since the time step of the traditional finite-difference time-domain (FDTD) method is limited by the small grid size, it is inefficient when dealing with the electromagnetic problems of multi-scale structures. Therefore, the explicit and unconditionally stable FDTD (US-FDTD) approach has been developed to break through the limitation of Courant–Friedrich–Levy (CFL) condition. However, the eigenvalues and eigenvectors of the system matrix must be calculated before the time iteration in the explicit US-FDTD. Moreover, the eigenvalue decomposition is also time consuming, especially for complex electromagnetic problems in practical application. In addition, compared with the traditional FDTD method, the explicit US-FDTD method is more difficult to introduce the absorbing boundary and plane wave. To solve the drawbacks of the traditional FDTD and the explicit US-FDTD, a new hybrid FDTD algorithm is proposed in this paper. This combines the explicit US-FDTD with the traditional FDTD, which not only overcomes the limitation of CFL condition but also reduces the system matrix dimension, and introduces the plane wave and the perfectly matched layer (PML) absorption boundary conveniently. With the hybrid algorithm, the calculation of the eigenvalues is only required in the fine mesh region and adjacent coarse mesh region. Therefore, the calculation efficiency is greatly enhanced. Furthermore, the plane wave and the absorption boundary introduction of the traditional FDTD method can be directly utilized. Numerical results demonstrate the effectiveness, accuracy, stability, and convenience of this hybrid algorithm.

An Efficient Crosstalk Model For Coupled Multiwalled Carbon Nanotube Interconnects

In this paper, the crosstalk effects in coupled multiwalled carbon nanotube (MWCNT) interconnects have been analyzed. An unconditionally stable finite-difference time-domain (USFDTD) technique has been used for the crosstalk model. The in_phase delay, out_phase delay, and crosstalk noise for coupled interconnect lines have been determined. It is observed that crosstalk effect is less severe in MWCNT interconnects compared to the conventional copper interconnects. The results of the proposed model have been verified with the conventional FDTD technique, hailey simulation program with integrated circuit emphasis (HSPICE), and feature selective validation. For transient analysis, the proposed model on an average consumes 46% lesser CPU runtime as compared to the conventional FDTD technique. Further, stress and electro-migration effects have been analyzed for copper and MWCNT interconnects. The mean time to failure of MWCNT interconnects is found to be superior than that of copper interconnects.

An Unconditionally Stable FDTD Model for Crosstalk Analysis of VLSI Interconnects

In this paper, an unconditionally stable finite-difference time-domain (US-FDTD) model is proposed for the crosstalk noise analysis of coupled very large scale integration interconnects. The accuracy of the proposed model is validated against the conventional FDTD model and HSPICE. It is observed that the proposed model is as accurate as the conventional FDTD and HSPICE. It is also observed that the stability of the proposed model is not constrained by the Courant–Friedrichs–Lewy stability condition. Depending on the time-step size, the proposed model can be up to $100\times $ faster than the conventional FDTD.

A Compact Unconditionally Stable Method for Time-Domain Maxwell's Equations

Higher order unconditionally stable methods are effective ways for simulating field behaviors of electromagnetic problems since they are free of Courant-Friedrich-Levy conditions. The development of accurate schemes with less computational expenditure is desirable. A compact fourth-order split-step unconditionally-stable finite-difference time-domain method (C4OSS-FDTD) is proposed in this paper. This method is based on a four-step splitting form in time which is constructed by symmetric operator and uniform splitting. The introduction of spatial compact operator can further improve its performance. Analyses of stability and numerical dispersion are carried out. Compared with noncompact counterpart, the proposed method has reduced computational expenditure while keeping the same level of accuracy. Comparisons with other compact unconditionally-stable methods are provided. Numerical dispersion and anisotropy errors are shown to be lower than those of previous compact unconditionally-stable methods.

High-Order Split-Step Unconditionally-Stable FDTD Methods and Numerical Analysis

High-order split-step unconditionally-stable finite-difference time-domain (FDTD) methods in three-dimensional (3-D) domains are presented. Symmetric operator and uniform splitting are adopted simultaneously to split the matrix derived from the classical Maxwell's equations into four sub-matrices. Accordingly, the time step is divided into four sub-steps. In addition, high-order central finite-difference operators based on the Taylor central finite-difference method are used to approximate the spatial differential operators first, and then the uniform formulation of the proposed high-order schemes is generalized. Subsequently, the analysis shows that all the proposed high-order methods are unconditionally stable. The generalized form of the dispersion relations of the proposed high-order methods is carried out. Moreover, the effects of the mesh size, the time step and the order of schemes on the dispersion are illustrated through numerical results. Specifically, the normalized numerical phase velocity error (NNPVE) and the maximum NNPVE of the proposed second-order scheme are lower than that of the alternating direction implicit (ADI) FDTD method. Furthermore, the analysis of the accuracy of the proposed methods is presented. In order to demonstrate the efficiency of the proposed methods, numerical experiments are presented.

An unconditionally stable FDTD method based on wave equation

AbstractAn unconditionally stable finite‐difference time‐domain (US‐FDTD) method based on wave equation is introduced by making use of Laguerre polynomials as basis functions for expanding field components in time. This new wave‐equation‐based FDTD scheme is not only unconditionally stable but also requires less memory usage. Comparisons among the traditional FDTD, the conventional Laguerre‐polynomial US‐FDTD, and this proposed scheme are presented in the numerical examples in terms of the memory usage and computational time. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 529–532, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24101

Unconditionally stable FDTD formulation with UPML-ABC

A new unconditionally stable finite-difference time-domain (US-FDTD) formulation is established in combination with the uniaxial anisotropic perfectly matched layer absorbing boundary condition. This approach exhibits improved absorbing performance yet maintains unconditional stability. Numerical results show that the reflection error of this scheme is limited even when the time-step size is beyond the Courantndash;Friedrichndash;Levy stability bound, and the absorbing performance is better than that of the US-FDTD with the dispersive boundary condition.

Analyses of bounces on power distribution networks using an unconditionally stable finite-difference time-domain method

An unconditionally stable finite-difference time-domain (US-FDTD) method is utilized for analyzing the bounces on structures of power distribution networks (PDNs), which is a critical issue in the electromagnetic compatibility analysis of mobile devices. The US-FDTD method does not utilize the explicit leapfrog time scheme of conventional FDTD method and can solve problems with fine structures well, such as via, thin material and so on. By using this full-wave method, electromagnetic fields between power/ground plane pairs are analyzed and discontinuities of through-hole vias are taken into account in the modeling of PDNs.

A Compact Unconditionally Stable FDTD Method

A novel compact unconditionally stable finite-difference time-domain (US-FDTD) method is introduced. This method utilizes proper intermediate field components to simplify the original unconditionally stable Crank-Nicolson (CN) scheme. The unconditionally stability of the proposed compact US-FDTD method is analytically proven. Numerical results are included to illustrate the stability, accuracy, and efficiency of the proposed compact US-FDTD

More accurate and efficient unconditionally stable FDTD method

A more accurate and efficient unconditionally stable finite-difference time-domain (US-FDTD) method is proposed. The two key points of the proposed US-FDTD method are: defining the field components at only n and (n+1) time steps; and arranging the left and right hands of the original updating equations to be as accurate (in respect of time) as possible. It is demonstrated that the US-FDTD method is more efficient (in both computer memory and CUP time) and more accurate than the recently developed ADI-FDTD method.