Stable FDTD Method Research Articles

A New Unconditionally Stable FDTD Method Based on Artificial Neural Network

A New Unconditionally Stable FDTD Method Based on Artificial Neural Network

Performance investigation of doped multi-layer graphene nanoribbon as interconnects in modern technology nodes

In this paper, the performance of intercalation doped multilayer graphene nanoribbons (MLGNR) with modern technology nodes is meticulously investigated. An unconditionally stable FDTD method is used to analyze the transient output of the circuit. Several cases of MLGNR interconnects under different doping materials, stacking directions and contact modes have been discussed. With multiple experiments carried out, it is shown that the Li-doped MLGNR interconnect with vertical stacking orientation has the most outstanding performance, which has the least delay compared with the traditional Cu interconnect and other counterparts in 3-nm and 5-nm nodes. In summary, the Li-doped vertically stacked MLGNR is very promising for carbon nano interconnects in the next generation of integrated circuits.

Crosstalk optimization and gate oxide reliability analysis in intercalation doped MLGNR with reduced vertical thickness

In this paper, the performance of intercalation doped multilayer graphene nanoribbons (MLGNR) with reduced vertical thickness is investigated, and the impact of crosstalk on latency and gate oxide reliability is analyzed. An unconditionally stable FDTD method is used to analyze the transient output of the circuit. Several cases of MLGNR with reduced vertical thickness under different doping materials, stacking directions and contact modes have been discussed. The experimental data show that the Li-doped MLGNR interconnect with horizontal stacking and side contact (SC) has the most outstanding performance, and the delay fluctuation caused by crosstalk is improved by 17.8 % ∼ 68.1 % compared with the Cu interconnect. When specularity p = 0.2, the PDCP (power delay crosstalk product) is found 44.2 % ∼ 61.5 % lower than the Cu interconnect. In addition, the AFR (average failure rate) has also been investigated, and the data showed that the AFR of Li-doped SC-MLGNR remained lowest among all interconnects discussed, for comparison the Cu interconnect is 4.2–5 times larger than the former. In summary, the vertical thickness reduced Li-doped horizontally stacked SC-MLGNR is very promising as carbon nano interconnects in the next generation of integrated circuits.

The Unconditionally Stable Associated Hermite FDTD Method With Dielectric Coating Thin Wires Model

The Unconditionally Stable Associated Hermite FDTD Method With Dielectric Coating Thin Wires Model

An HIE‐FDTD algorithm for dispersive media with modified Lorentz model

AbstractIn this letter, a hybrid implicit–explicit finite difference time domain (HIE‐FDTD) method is developed to simulate general dispersive media with modified Lorentz model. The dispersive media is described through modified Lorentz model and is incorporated into the HIE‐FDTD method by two different auxiliary differential equations (ADEs). One ADE establishes the relationship between the electric displacement and electric field intensity and the other one establishes the connection between the electric current density and electric field intensity. Numerical examples are conducted and it can be seen from the numerical results that the proposed algorithm can simulate dispersive media correctly and also improve computational efficiency compared with the FDTD method and one unconditionally stable FDTD method.

The Unconditionally Stable Associated Hermite FDTD Method With Thin Wire Modeling

The Unconditionally Stable Associated Hermite FDTD Method With Thin Wire Modeling

An explicit and absolutely stable FDTD method for electromagnetic analysis

An explicit and absolutely stable FDTD method for electromagnetic analysis

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.

Stable 3D FDTD method for arbitrary fully electric and magnetic anisotropic Maxwell's equations

AbstractWe have developed a new fully anisotropic 3D FDTD Maxwell solver for arbitrary electrically and magnetically anisotropic media for piecewise constant electric and magnetic materials that are co‐located over the primary computational cells. Two numerical methods were developed that are called nonaveraged and averaged methods, respectively. The nonaveraged method is first‐order accurate, while the averaged method is second‐order accurate for smoothly‐varying materials and reduces to first order for discontinuous material distributions. For the standard FDTD field locations with the co‐location of the electric and magnetic materials at the primary computational cells, the averaged method required development of the different inversion algorithms of the constitutive relations for the electric and magnetic fields. We provide a mathematically rigorous stability proof followed by extensive numerical testing that includes long‐time integration, eigenvalue analysis, tests with extreme, randomly placed material parameters, and various boundary conditions. For accuracy evaluation, we have constructed a test case with an explicit analytic solution. Using transformation optics, we have constructed complex, spatially inhomogeneous geometrical object with fully‐anisotropic materials and a large dynamic range of and , such that a plane wave incident on the object is perfectly reconstructed downstream.

A new paralleling-in-order based unconditionally stable FDTD method using Legendre polynomials

A new paralleling-in-order based unconditionally stable FDTD method using Legendre polynomials

An Unconditionally Stable Cylindrical FDTD Method to Analyze the EM Ground Wave Propagation

We extended the unconditionally stable associated Hermite (AH) FDTD method to the cylindrical coordinate system for analyzing the electromagnetic (EM) ground wave propagation. With AH domain differentiate operator technology and paralleling-in-order solution scheme, the cylindrical time-domain Maxwell equations with complex frequency shifted perfectly matched layer (CFS-PML) are transformed to AH domain generating a five-point banded equation, which also unified the formula from the central axis of cylinder. The numerical results represent the accuracy and efficiency of the proposed method when comparing for the conventional FDTD method.

Fast Modeling of Terahertz Plasma-Wave Devices Using Unconditionally Stable FDTD Methods

Modeling of terahertz plasmonic device is a multiscale and multiphysics problem that requires fine mesh in the electron transport regions, inevitably leading to long simulation times. In this paper, we tackle this problem by employing unconditionally stable FDTD methods for these simulations. Specifically, we present alternating direction implicit (ADI) FDTD and iterative-ADI-FDTD based efficient multiphysics model that integrate hydrodynamic equations and Maxwell's equations for modeling terahertz plasmonic devices. Using the proposed methods, we demonstrate 50% time-reduction with a nominal 3% errors in the solutions. Faster times may also be achieved at higher cost to solution-accuracy, suggesting an ability to adjust time-costs and accuracy, useful for different terahertz modeling scenarios.

Improved Unconditionally Stable FDTD Method for 3-D Wave-Propagation Problems

The findings of this paper prove that the direct implementation of fourth-order operators in the alternating-direction-implicit finite-difference time-domain algorithm is not the most consistent way to improve its accuracy. Instead of applying the standard expressions, a methodology that exploits the scheme’s dispersion relation is introduced, so that space-time errors are balanced as equally as possible. After applying a matching-terms approach, new operator coefficients are extracted that depend on cell shape and time-step size. The resulting scheme offers an order of magnitude smaller error over practically all frequencies of interest, verifying the successful implementation of dispersion-reducing practices in this unconditionally stable technique.

An Efficient Unconditionally Stable FDTD Method for Analyzing Composite Right Left Handed Transmission Line

For analyzing the composite right/left-handed (CRLH) transmission line (TL) problems, an efficient unconditionally stable (US) finite-difference time-domain method is proposed in the letter. First, based on Kirchhoff's voltage law and Kirchhoff's current law, the CRLH TL equations are derived and rewritten in matrix form. Then, by adopting the Crank-Nicolson time split technique, and carrying out some transformations to achieve an equivalent formulation, the US scheme for the implementation of the CRLH TL equations can be obtained. Two numerical examples are used to validate the efficiency and accuracy of the proposed method in analyzing a CRLH TL and pure left-handed TL.

A New Marching-on-in-Order Based 2-D Unconditionally Stable FDTD Method

A New Marching-on-in-Order Based 2-D Unconditionally Stable FDTD Method

Three-dimensional efficient dispersive alternating-direction-implicit finite-difference time-domain algorithm using a quadratic complex rational function.

Efficient unconditionally stable FDTD method is developed for the electromagnetic analysis of dispersive media. Toward this purpose, a quadratic complex rational function (QCRF) dispersion model is applied to the alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method. The 3-D update equations of QCRF-ADI-FDTD are derived using Maxwell's curl equations and the constitutive relation. The periodic boundary condition of QCRF-ADI-FDTD is discussed in detail. A 3-D numerical example shows that the time-step size can be increased by the proposed QCRF-ADI-FDTD beyond the Courant-Friedrich-Levy (CFL) number, without numerical instability. It is observed that, for refined computational cells, the computational time of QCRF-ADI-FDTD is reduced to 28.08 % of QCRF-FDTD, while the L2 relative error norm of a field distribution is 6.92 %.

Unconditionally Stable FDTD Method Based on LOD Scheme for Analysis of 2-D Periodic Structures

For modeling periodic structures at oblique incidence, an unconditionally stable finite-difference time-domain technique is presented by applying the locally one-dimensional (LOD) scheme to the field transformation technique. By splitting the space operator matrix in an appropriate way, the transformed Maxwell's equations can be subdivided into two sub-steps for an efficient implementation. The accuracy and efficiency of the proposed method are verified by comparing with the results of the reference [4] and the split-field method respectively.

Computation of Optical Force on Nanoparticles Using Locally Non-Orthogonal Overlapping Yee FDTD Method

In this paper, a locally non-orthogonal overlapping Yee (OY) FDTD method is proposed in order to accurately calculates the optical force on dielectric and dispersive nanoparticles. It extends our previous work to geometries with sharp corners and dispersive materials. In addition to consistently achieving the smallest errors in comparison to the standard FDTD method, the OY approach is a stable non-orthogonal FDTD method that attains second-order convergence when sharp corners are present.

Weakly conditionally stable FDTD method for analysis of 3D periodic structures at oblique incidence

For analysing the 3D periodic structures at the oblique incident, a weakly conditionally stable finite-difference time-domain method is proposed by applying the Crank-Nicolson (CN) scheme to the field transformation technique. By splitting the space operator matrix in a special way, the transformed Maxwell's equations can be subdivided into two sub-steps for an efficient implementation. The proposed method does not need to introduce additional field components to handle the extra time terms and the time step size is only determined by one space discretisation.

The Unconditionally Stable One-Step Leapfrog ADI-FDTD Method and Its Comparisons With Other FDTD Methods

One of the major hurdles that prevent the recently developed alternating-direction-implicit finite-difference time- domain (ADT-FDTD) method from being widely used is its relatively large computational expenditures due to its sub-step computations. To address the issue, a reformulation of the unconditionally stable one-step leapfrog ADI-FDTD method and its comparisons with other FDTD methods are presented in this letter. It is found that the one-step method requires less amount of memory and CPU time than the current unconditionally stable FDTD methods and the similar memory requirement and less CPU time (when the time step is chosen to be adequately large) than the conventional FDTD method. In other words, when the unconditionally stable FDTD methods are required to solve electromagnetic problems, one is strongly recommended to use the one-step leapfrog method presented.