ADI-FDTD algorithm in curvilinear co-ordinates

The alternating direction implicit (ADI) scheme has been successfully applied to the finite-difference time-domain (FDTD) method to achieve an unconditionally stable algorithm. The ADI-FDTD method is extended to the curvilinear co-ordinate system to form an alternating direction implicit nonorthogonal FDTD (ADI-NFDTD) method. The numerical results show that the proposed ADI-NFDTD algorithm demonstrates better late time stability compared to the conventional NFDTD scheme.     

An Improved Implicit Split-Step Algorithm for Dispersive Band-Limited FDTD Applications

An improved unconditionally stable envelope finite difference time domain (FDTD) algorithm is presented for modeling open region dispersive band-limited electromagnetic applications. The algorithm is based on incorporating the split-step implicit FDTD scheme into the stretched coordinates perfectly matched layer absorbing boundary conditions. Numerical examples carried out in 2-D domains are included to show the validity of the proposed formulations.      

二维无条件稳定时域有限差分方法

基于半隐式的Crank-Nicolson差分格式给出了一种无条件稳定时城有限差分方法。和传统FDTD法中采用的显式差分格式不同，对Maxwell方程组采用半隐式差分格式，在时间和空间上仍然是二阶精确的。但时间步长不再受稳定性条件的限制，只需考虑数值色散误差对其取值的制约。利用分裂场完全匹配层吸收边界截断计算空间，为保证PML空间的无条件稳定性，其方程也采用半隐式差分格式。数值结果表明相同条件下US-FDTD方法与传统FDTD方法的计算精度是相同的，而且在增大时间步长时US-FDTD方法是稳定的和收敛的。可以预见US-FDTD方法在模拟具有电小结构问题时具有实际意义。     

Complex Envelope Crank-Nicolson Nearly PML Algorithm for the Left-handed Material FDTD Simulations

Unconditionally stable complex envelope (CE) absorbing boundary conditions (ABCs) are presented for truncating left handed material (LHM) domains. The proposed algorithm is based on incorporating the Crank Nicolson (CN) scheme into the CE finite difference time domain (FDTD) implementations of the nearly perfectly matched layer (NPML) formulations. The validity of the formulations is shown through numerical example carried out in one dimensional Lorentzian type LHM FDTD domain.     

区域分解时域有限差分方法(DD-FDTD)及其在散射问题中的应用

本文提出一种区域分解的时域有限差分算法(DD-FDTD).依据待解问题的特点,把待解问题分解为几个子区域,在各个子区域中,采用适合于该区域的共形网格进行划分计算,通过一种有效的信息传递方案,把各个子区域综合起来,获得原问题的解.通过采用这种方法,一个复杂的问题可以得到简化,从而变得适于求解,同时,共形网格和精确的信息传递方案的使用,大幅度提高了计算精度.文中,用该算法对二维电磁散射问题进行了分析计算,获得了精确的计算结果.     

Three-Dimensionally Nonorthogonal Alternating-Direction Implicit Finite-Difference Time-Domain Algorithm for the Full-Wave Analysis of Microwave Monolithic Circuit Devices

An alternating-direction implicit finite-difference time-domain (FDTD) algorithm is applied to the full wave analysis of microwave integrated circuit devices. A 3-D multidomain method is developed in nonorthogonal coordinates. Nonorthogonal grids are only used for the anomalistic regions of a complex structure, whereas the standard FDTD lattice is used for the other regions. By using the Jacobian coordinate transformation, curvilinear coordinates can be converted into conventional FDTD format expediently. The perfectly matched layer is used to truncate the boundary. Accurate griddings using the new scheme are obtained, and the complexity of the algorithm is minimal. To illustrate the theory, a sinusoidal plane wave and a Gaussian pulse that propagate through a localized nonorthogonal grid space is used, and the stability of our code is examined. A newly developed compact microstrip bandpass filter is analyzed using the proposed method. The simulated results agree very well with measurements. As compared to other nonorthogonal FDTD (NFDTD) method, the proposed algorithm is much more efficient than other NFDTD counterpart when complex structures are analyzed.      

Unconditionally Stable Z-Transform ADI-PML Algorithm for Lorentzian Double Negative Meta-Materials

Unconditionally stable formulations of the anisotropic perfectly matched layer (APML) are presented for truncating double negative (DNG) meta-material finite difference time domain (FDTD) grids. In the proposed formulations, the Z-transform theory is employed in the alternating direction implicit FDTD (ADI-FDTD) scheme to obtain update equations for the field components in the DNG meta-material domains. Numerical examples carried out in one dimensional Lorentzian type DNG meta-material domains are included to show the validity of the proposed formulations.     

A hybrid 2-D ADI-FDTD subgridding scheme for modeling on-chipinterconnects

This paper presents a novel technique for extracting the propagation characteristics of on-chip interconnects. A hybrid two-dimensional subgridding scheme, based on a combination of the finite-difference time-domain (FDTD) method and the alternating-direction implicit (ADI-)FDTD technique, is utilized. The ADI-FDTD scheme is used for fine grid in the vicinity of the metallic etch, while the coarse FDTD grid is used outside this region. The advantage of the ADI-FDTD scheme is that it can be synchronized with the time marching step employed in the coarse FDTD scheme, obviating the need for the temporal interpolation of the fields in the process. This helps to render the hybrid ADI-FDTD subgridding scheme to be more efficient than the conventional FDTD subgridding algorithm in terms of the run time. The phase and attenuation constants of the dominant mode of a lossy stripline are computed by the proposed scheme to validate the technique     

A 3-D precise integration time-domain method without the restraints of the courant-friedrich-levy stability condition for the numerical solution of Maxwell's equations

In this paper, a new three-dimensional time-domain method for solving vector Maxwell's equations, called the precise-integration time-domain (PITD) algorithm, is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on the precise-integration technique. It is shown that this method is quite stable even when the CFL condition is not satisfied. Although the memory requirement of the PITD method is much larger than that of the finite-difference time-domain (FDTD) method, this new algorithm is very appealing since the time step used in the simulation is no longer restricted by stability. As a result, computation speed can be improved. Therefore, if the minimum cell size in the computational domain is required to be much smaller than the wavelength, this new algorithm is more efficient than the FDTD scheme. Theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness and efficiency of the method. It is found that the accuracy of the PITD is independent of the time-step size.     

On the numerical errors in the 2D FE/FDTD algorithm for different hybridization schemes

Numerical experiments are carried out to study the accuracy of the two-dimensional Finite-Element/Finite-Difference Time-Domain (FE/FDTD) hybrid algorithm with three different hybridization schemes. The physical space is split into two domains viz., the finite difference (FD) and finite element (FE) domains. In the FD domain, a uniform Cartesian grid is used and in the FE domain, triangular elements with edge vector basis functions are used. Newmark-/spl beta/ scheme is used for temporal discretization in the FE domain. The unphysical reflections introduced by the FE domain for the different schemes are compared by computing the 2-D radar cross section of the FE domain surrounded by the FD domain. Computed results of scattering by a PEC circular cylinder for TE/sub z/ incidence using the three schemes and the traditional FDTD algorithm are presented.     

A higher order (2,4) scheme for reducing dispersion in FDTDalgorithm

A finite-difference time-domain (FDTD) scheme with second-order accuracy in time and fourth-order in space is discussed for the solution of Maxwell's equations in the time domain. Compared with the standard Yee (1966) FDTD algorithm, the higher order scheme reduces the numerical dispersion and anisotropy and has improved stability. Dispersion analysis indicates that the frequency band in which the higher order scheme yields an accurate solution is widened on the same grid, this means a larger space increment can be chosen for the same excitation. Numerical results show the applications of the scheme in modeling wide-band electromagnetic phenomena on a coarse grid     

A hybrid implicit-explicit FDTD scheme for nonlinear opticalwaveguide modeling

A hybrid implicit-explicit finite-difference time-domain (FDTD) method for solving the wave equation in nonlinear optical waveguiding structures is proposed. The new scheme combines the computational simplicity of the explicit scheme in linear medium regions with the superior stability property of the partially implicit scheme in regions of nonlinear materials, thus eliminating potential problems of instability associated with nonlinearity. Simulation results for Kerr-type nonlinear slab waveguides and corrugated waveguides are presented and compared with those obtained using the conventional noniterative FDTD scheme     

Analyzing the stability of the FDTD technique by combining the vonNeumann method with the Routh-Hurwitz criterion

This paper addresses the problem of stability analysis of finite-difference time-domain (FDTD) approximations for Maxwell's equations. The combination of the von Neumann method with the Routh-Hurwitz criterion is proposed as an algebraic procedure for obtaining analytical closed-form stability expressions. This technique is applied to the problem of determining the stability conditions of an extension of the FDTD method to incorporate dispersive media previously reported in the literature. Both Debye and Lorentz dispersive media are considered. It is shown that, for the former case, the stability limit of the conventional FDTD method is preserved. However, for the latter case, a more restrictive stability limit is obtained. To overcome this drawback, a new scheme is presented, which allows the stability limit of the conventional FDTD method to be maintained     

Simple and Efficient PML Algorithm for Truncating Nonlinear FDTD Domains Based on the <Emphasis Type="Italic">Z</Emphasis>-Transform Method

Based on the Z-transform method, a simple, efficient and unsplit-field implementation of the Stretched Coordinate Perfectly Matched Layer (SC-PML) is proposed for truncating the nonlinear dispersive Finite Difference Time Domain (FDTD) lattices. In addition, the nonlinear FDTD formulations using the Z-transform method are reformulated with the advantage of a simple derivative process. The proposed algorithm is validated through two numerical examples carried out in one dimensional and two dimensional domains which include Lorentz dispersion as well as Kerr and Raman nonlinearities.     

Digital filtering technique for the FDTD implementation of the anisotropic perfectly matched layer

A new algorithm is presented for the finite difference time domain (FDTD) implementation of the anisotropic perfectly matched layer (PML) using the digital signal processing. The algorithm is based on modeling the anisotropic PML region as a set of infinite-impulse response (IIR) digital filters. The advantage of the proposed method is that it allows direct FDTD implementation of Maxwell's equations in the PML region. In addition, the formulations are implemented using D and B fields rather than E and H, and this allows the PML to be independent from the material properties of the FDTD computational domains. Numerical tests have been carried out in two dimensions to validate the formulations.     

Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method

In order to deal with the stability problem restricted by the finite-difference time-domain (FDTD) and conventional pseudospectral time domain (PSTD), the multidomain PSTD algorithm based on alternating-direction implicit (ADI) technique is proposed in this paper. This algorithm improves the stability and efficiency of conventional PSTD, while it maintains the accuracy and flexibility of conventional PSTD for an accurate treatment of arbitrarily curved objects. A compact matrix form is derived to effectively describe two-dimensional ADI multidomain pseudospectral time domain (ADI-MPSTD) algorithm. Numerical results show an excellent agreement with analytical solutions as well as results obtained by the FDTD algorithm, and fully demonstrate a remarkable improvement in stability and efficiency.     

基于FDTD算法的新型亚网格技术

提出了一种基于空间滤波（Spatial Filtering-Finite-Difference Time-Domain,SF-FDTD）算法的亚网格技术,使得FDTD算法的Courant-Friedrich-Levy（CFL）稳定性条件可通过空间频域滤波操作得以提高,从而获得高稳定度FDTD算法.进一步将SF-FDTD算法应用到亚网格技术中,可使亚网格区域时间步长的选取取与粗网格一致,从而极大地提高了计算效率.数值计算结果表明,在求解带有精细结构的电磁问题上,所提算法具有较高的准确性和有效性.     

A Modified High Order FDTD Method Based on Wave Equation

A modified (2M, 4) scheme of the high-order two-dimensional finite-difference time-domain (FDTD) method based on wave equation is proposed. It has the fourth-order accuracy in the time domain using the symplectic integrator propagator, and the 2M-order accuracy in the space domain using the discrete singular convolution method. The distinctive features between the modified scheme and the traditional (2M, 4) FDTD based on Yee algorithm are listed as follows. First, the modified scheme is based on the wave equation. Second, the computational region is discretized by uniform mesh rather than the Yee mesh. Third, the modified scheme costs less memory than the Yee algorithm because fewer field elements are involved in computation. Numerical examples are provided to validate its accuracy and effectiveness     

Unconditionally stable D-H FDTD formulation with anisotropic PMLboundary conditions

An unconditionally stable finite difference time domain (FDTD) method based on a D-H formulation and the recently proposed alternating-direction-implicit (ADI) marching scheme is presented. The advantage of the D-H algorithm over the conventional E-H is the possibility to easily implement an unsplit field components formulation of the PML absorbing boundary condition that is independent from the background material used in the FDTD grid. The method allows therefore immersing any dielectric in the PML layers without any special consideration, and is amenable for models truncation often used in biomedical simulations. Furthermore, the proposed scheme can be extended to account for frequency dispersive dielectrics     

碰撞等离子体的高阶FDTD算法

给出了电磁波在均匀、碰撞等离子体中传播的四阶时间和四阶空间FDTD算法.该算法比Yee氏FDTD算法每一个网格每一维增加一个存储单元,与常规的二阶等离子体FDTD算法相同.由于采用四阶时间和四阶空间近似,因此该算法能有效地减小数字色散误差,其频带宽度比二阶算法的频带宽度更宽.为了验证该高阶算法的正确性,对均匀、碰撞等离子体平板的电磁波反射系数进行了计算,并与解析结果、二阶FDTD计算结果进行了比较,证明了该算法的高效和精确.