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 hybrid Yee algorithm/scalar-wave equation approach

In this paper, two alternate formulations of the Yee algorithm, namely, the finite-difference time-domain (FDTD) vector-wave algorithm and the FDTD scalar-wave algorithm are examined and compared to determine their relative merits and computational efficiency. By using the central-difference divergence relation the conventional Yee algorithm is rewritten as a hybrid Yee/FDTD scalar-wave algorithm. It is found that this can reduce the computation time for many 3-D open geometries, in particular planar structures, by approximately two times as well as reduce the computer-memory requirements by approximately one-third. Moreover, it is demonstrated both mathematically and verified by numerical simulation of a coplanar strip transmission line that this hybrid algorithm is entirely equivalent to the Yee algorithm. In addition, an alternate but mathematically equivalent reformulation of the Enquist-Majda absorbing boundary condition based on the normal field component (relative to the absorbing boundary wall) is given to increase the efficiency of the hybrid algorithm in the modeling of open region problems. Numerical results generated by the hybrid Yee/scalar-wave algorithm for the Vivaldi antenna are given and compared with published experimental work     

基于SMP集群系统的MPI—OpenMP混合并行FDTD算法研究

针对基于MPI的传统FDTD并行算法存在的缺点,提出了优化的FDTD两级化并行算法。结合MPI和OpenMP编程模型的特点,实现了基于SMP集群系统平台的MPI-OpenMP混合编程模型的两种并行FDTD算法。在实验室搭建的SMP集群系统平台上,通过对一金属长方体的散射问题分析,把混合编程算法同基于MPI的FDTD并行算法进行了比较。结果表明,混合并行算法具有更好的加速比和带宽利用率。     

并行FDTD-UTD方法分析机载相控阵天线

利用时域有限差分法(FDTD)-UTD(一致性几何绕射理论)混和算法分析机载相控阵天线的辐射方向图.将复矢量场作为FDTD方法和UTD方法的接口,提出FDTD-UTD混和算法解决机载相控阵天线辐射问题.首先利用并行FDTD方法通过全波分析得到精确的相控阵的辐射复矢量场,然后将此结果作为源代入UTD算法来预测相控阵受机体的影响.结果表明该方法可以有效地解决机裁相控阵辐射分析问题.     

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     

Hybrid finite-difference/finite-volume time-domain analysis formicrowave integrated circuits with curved PEC surfaces using anonuniform rectangular grid

In this paper, we present a hybrid algorithm that combines the finite-difference time-domain (FDTD) and finite-volume time-domain (FVTD) methods to analyze microwave integrated-circuit structures that may contain curved perfect electric conductor (PEC) surfaces. We employ the conventional nonuniform FDTD in regions where the objects are describable with a rectangular mesh, while applying the FVTD method elsewhere where we need to deal with curved PEC configurations. Both the FDTD and FVTD quantities are defined in the mutually overlapping regions, and these fields from the respective regions are interpolated by using their nearest neighbors. We validate this algorithm by analyzing the scattering parameters of a stripline with one or more adjacent cylindrical vias, whose geometries are frequently encountered in printed-circuit-board designs. It is found that the hybrid FDTD-FVTD approach requires little increase in central processing unit time and memory in comparison to the conventional FDTD, while its computational accuracy is significantly improved over a wide range of frequencies. Specifically, this accuracy is found to be comparable to that achieved by doubling the mesh density of the staircased FDTD     

GPOF在FDTD近远场外推中的应用及编程实现*

该文针对FDTD近远场外推中时域解收敛慢和运算量大等问题,改进了FDTD求解方向图的方法.其核心思想是:FDTD近场计算时,只计算前一段时间外推面上的数据,利用GPOF法估算后面时间的数据.在计算过程中,利用奈奎斯特原理,减少了时间和空间上的采样点数,大大节省了运算时间.最后将数值结果与商业软件FEKO与HFSS的结果进行比较,验证了算法的有效性.     

Analyzing electromagnetic structures with curved boundaries onCartesian FDTD meshes

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by traditional FDTD formulas. Therefore, this new algorithm is more efficient than general nonorthogonal FDTD schemes in terms of computer resources such as memory and central processing unit (CPU) time. Simulation results are presented and compared to those using other methods     

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.      

A new FDTD algorithm based on alternating-direction implicit method

In this paper, a new finite-difference time-domain (FDTD) algorithm is proposed in order to eliminate the Courant-Friedrich-Levy (CFL) condition restraint. The new algorithm is based on an alternating-direction implicit method. It is shown that the new algorithm is quite stable both analytically and numerically even when the CFL condition is not satisfied. 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 conventional FDTD schemes in terms of computer resources such as central-processing-unit time. Numerical formulations are presented and simulation results are compared to those using the conventional FDTD method     

采用FDTD/FVTD混合算法分析蝶形微带天线

用FDTD和FVTD混合算法分析了蝶形微带天线的反射损失.在适于矩形网格的区域采用常规的非均匀FDTD算法,在微带贴片天线的斜边或PEC弯曲表面处采用FVTD算法,重叠区域的场通过邻近场的线性插值得到.程序仿真和实际测量结果的比较表明在较宽的频带内,该算法在不损失精度,不显著增加CPU时间和内存的情况下,极大地降低了常规FDTD所要求的网格密度.     

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 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.     

FDTD-PWS Scheme and Its Application to Analysis of Focusing Properties of Dielectric Lens

The focusing properties of lens are studied by a hybrid scheme that involves the finite-difference time-domain (FDTD) method for the aperture-plane field computation and the plane wave spectrum (PWS) method for the transformation from the aperture-plane field to the focal-plane field. To demonstrate the accuracy and efficiency of this new scheme, a Ka-band lens antenna is simulated and fabricated as an example. Subsequently, the near-field-region and the Fresnel-region fields of this lens antenna are measured by the planar-near-field (PNF) method. It is found that the results obtained by the FDTD-PWS scheme are in good agreement with the measured data. Furthermore, the numerical results and the computational requirements of this new scheme are compared with those of the near-field to near-field (NF-NF) transformation, the aperture integration (AI) method, the geometrical optics (GO)-physical optics (PO) method, and the full FDTD simulation. Both the central processing unit (CPU) time and memory requirement can be reduced efficiently. Finally, the effects of several fundamental issues, including spatial sample parameters, lens material, operating frequency, and designed focal length, on the accuracy of the proposed scheme and on the focusing properties of the lens are investigated.      

Unconditionally Stable Bilinear Transformation FDTD Algorithm for Modeling Double-Negative Meta-material Electromagnetic Problems

Accurate and unconditionally stable finite difference time domain (FDTD) algorithm is presented for modeling electromagnetic wave propagation in double-negative (DNG) meta-material domains. The proposed algorithm is based on incorporating the Bilinear transformation technique into the FDTD implementations of Maxwell’s equations. The stability of the proposed approach is studied by combining the von Neumann method with the Routh-Huwitz criterion and it has been observed that the proposed algorithm is free from the Courant-Friedrichs-Lewy (CFL) stability limit of the conventional FDTD scheme. Furthermore, the proposed algorithm is incorporated with the split-step FDTD scheme to model two-dimensional problems. Numerical examples carried out in one and two dimensional domains are included to show the validity of the proposed algorithm.     

Passive equivalent circuit of FDTD: an application to subgridding

The finite difference time domain (FDTD) method gives accurate results for many problems but uses a large amount of computer memory and time. This can be reduced by using subgrids (fine grids) only around critical areas in the problem domain. The fields within the coarse and fine grids are found using standard FDTD equations, while at the boundary of the subgrid, interpolation of coarse grid fields is utilised. However, a simple interpolation as reported in literature exhibits late time instability. The authors present a stable scheme of updating the subgrid boundary fields by replacing the grid discontinuity with an equivalent circuit. The stability and accuracy of this new scheme is demonstrated through calculation of the cutoff wavelength of a dielectric slab loaded waveguide for various slab thickness     

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.     

基于STL文件的FDTD网格剖分算法

针对复杂目标的时域有限差分(finite-difference time-domain,FDTD)法计算,提出了一种将非结构化网格直接转化为Yee网格的改进算法.该算法在射线求交方法的基础上对射线方程与三角面元求交公式进行优化,实现了快速的目标网格生成,有效降低了计算复杂度并提升了剖分效率.通过介质球、军舰和F22飞机...     

Space-domain finite-difference and time-domain moment method for electromagnetic simulation

A hybrid time-domain numerical method based on finite-difference technique and moment method is proposed. Starting from Maxwell's differential equations, our method uses Yee's finite difference scheme in the space domain, but does not utilize the customary explicit leap-frog time scheme. Instead, in the time domain, the fields are expanded in a series of basis functions and treated by a moment method procedure. By choosing appropriate basis functions and testing functions, the conventional finite-difference time-domain (FDTD) formulation and the order-marching unconditionally stable FDTD scheme can be derived from our method as two special cases. Finally, we use triangle basis functions and Galerkin's testing procedure to get an implicit formulation. To verify the accuracy and efficiency of the new formulation, we compare the results with the FDTD method. Our method improves computational efficiency notably, especially for multiscale problems with fine geometric structures, which is restricted by stability constrain in the FDTD method.     

色散混合显隐式时域有限差分法的石墨烯仿真

应用色散混合显隐式时域有限差分（hybrid implicit-explicit finite-difference time-domain，HIE-FDTD）法分析了石墨烯的电磁特性.这种方法的时间步长大小不受石墨烯层的剖分网格大小的限制，数值算例表明，HIE-FDTD方法是一种精度较高的有效算法，它的计算时间比FDTD方案大大减少.数值计算结果显示，设计的石墨烯吸收体通过改变石墨烯片的化学势，可以有效地调整吸收体的吸收峰.同时发现，在太赫兹频率下石墨烯吸收体的吸收率显示出一定的周期性并呈现栅形特性，这一特性可以对石墨烯器件的设计生产提供一些思路.