An absorbing boundary condition for FDTD truncation using multiple absorbing surfaces

An absorbing boundary condition (ABC) is developed using multiple absorbing surfaces. This ABC is stable and efficient. It can be easily added in the finite-difference time-domain computer program. It also produces the same reflection as a higher order Higdon ABC and it is therefore comparable to the perfectly matched layer method.     

PML absorbing boundary condition for higher-order FDTD schemes

Higher-order finite difference time domain techniques make use of additional samples on the Yee grid in order to reduce the anisotropy, phase error and dispersion of the standard technique. The authors describe the implementation and verification of the perfectly matched layer (PML) absorbing boundary condition for the (2:4) technique     

A numerical absorbing boundary condition for finite difference andfinite element analysis of open periodic structures

In this paper we present a novel approach to deriving local boundary conditions, that can be employed in conjunction with the Finite Difference/Finite Element Methods (FD/FEM) to solve electromagnetic scattering and radiation problems involving periodic structures. The key step in this approach is to derive linear relationships that link the value of the field at a boundary grid point to those at the neighboring points. These linear relationships are identically satisfied not only by all of the propagating Floquet modes but by a few of the leading evanescent ones as well. They can thus be used in lieu of absorbing boundary conditions (ABCs) in place of the usual FD/FEM equations for the boundary points. Guidelines for selecting the orders of the evanescent Floquet modes to be absorbed are given in the paper. The present approach not only provides a simple way to derive an accurate boundary condition for mesh truncation, but also preserves the banded structure of the FD/FEM matrices. The accuracy of the proposed method is verified by using an internal check and by comparing the numerical results with the analytic solution for perfectly conducting strip gratings     

截断各向异性介质的修正NPML吸收边界条件

基于各向异性介质中的时域有限差分（Finite-Difference Time-Domain,FDTD）方法及近似完全匹配层（Nearly Perfect Match Layer,NPML）原理,提出一种截断各向异性介质的修正的NPML吸收边界条件.通过对Maxwell旋度方程中的空间偏导数进行坐标拉伸并结合空间插值方法,推导出易于在FDTD方法中实现的吸收边界公式.计算了电偶极子辐射场的反射误差,验证了这种吸收边界截断二维各向异性介质的有效性.三维算例中数值模拟了时谐场的相位分布,以及不同网格NPML吸收层随时间变化的反射误差.数值结果表明NPML吸收边界能有效吸收各向异性介质中的电磁波.     

The Bethe condition for thermionic emission near an absorbing boundary

The Bethe condition for thermionic emission in Schottky diodes is analysed in terms of the transport of carriers near the top of an absorbing barrier, under forward bias. It is shown that the usually accepted values of the drift velocity v_s and of the carrier density n(0) at the barrier maximum are not correct, v_s being underestimated by a factor of 2, and n(0) being overestimated by about the same factor. Fortunately, these discrepancies compensate in the product n(0)v_s, which yields the correct forward current. It is shown also by means of examples that the Bethe condition is satisfied only over a relatively limited range.     

应用UPML的FDTD法计算平面微带电路

采用非分裂式理想匹配层（UPML）的时域有限差分（FDTD）法对矩形微带天线及低通滤波器等微带电路进行了分析计算,给出了时域和频域的仿真结果。与其他的理想匹配层（PML）相比,UPML利用D和H,物理概念明确,将PML区域与FDTD计算域隔离开来,并且减少了PML吸收边界计算所占用的存储量。从仿真结果看,该方法有效且极大减少了迭代次数。     

WE—FDTD中近似吸收边界条件的角点计算

从线性插值思想出发研究波动方程时域有限差分法（WE—FDTD）中二维二阶近似吸收边界条件差分格式下矩形网格空间角点的场量计算方法。提出确定线性插值点位置的原则和线性插值点场量的迭代方法,考虑衰减因素进而计算角点的场量。     

WE-FDTD中近似吸收边界条件的角点计算

从线性插值思想出发研究波动方程时域有限差分法(WE-FDTD)中二维二阶近似吸收边界条件差分格式下矩形网格空间角点的场量计算方法。提出确定线性插值点位置的原则和线性插值点场量的迭代方法,考虑衰减因素进而计算角点的场量。     

Optimal design of PML absorbing boundary condition for improving wide-angle reflection performance

A method to optimise the angle reflection performance of Berenger's perfectly matched layer (PML) absorbing boundary condition for finite-difference time-domain (FDTD) method is described. By specifying the conductivity in each of the PML sublayers, the wide-angle reflection performance can be improved. To improve the angle reflection performance as well as to reduce the discretisation error characteristic due to the FDTD approximation, a two-step conductivity profile is used in PML. To obtain the optimal value for each conductivity profile, the micro-genetic algorithm method is employed. Using this method, good wide-angle reflection performance of PML is achieved.     

Numerically derived absorbing boundary condition for the solutionof open region scattering problems

An absorbing boundary condition is developed by means of a numerical approximation of the analytical behavior of the exact boundary condition. The boundary operator is more accurate than other analytically derived differential operators having the same order, and it can be applied to arbitrarily shaped scatterer geometries that can be handled most efficiently through the use of outer boundaries that conform to the body of the scatterer. Examples demonstrate the improvement in accuracy and efficiency achieved by the numerical boundary condition. The enhancement in accuracy is attributable to the inclusion of the evanescent harmonics behavior in the model     

APPLICATION OF THE PML ABSORBING BOUNDARY CONDITION TO FD-TD SIMULATION

The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach.     

Applicability of the PML absorbing boundary condition to dielectricanisotropic media

The authors study the applicability of Berenger's perfect matching layer (PML) absorbing boundary condition to match waves propagating on anisotropic media. Concrete conditions for some special cases are obtained, although no perfect matching can be achieved for the most general case     

An unsplit formulation of the Berenger's PML absorbing boundary condition for FDTD meshes

An unsplit formulation of the Berenger's perfectly matched layer absorbing boundary condition (PML ABC) for finite-difference time-domain (FDTD) meshes is presented. This unsplit formulation uses the conventional E-H algorithm, but does not require the E and H fields to be split. The proposed formulation is memory-efficient like that of the previous unsplit PML following the theory of Sacks. This unsplit formulation is easy to be implemented, and many useful modification to the Berenger's PML can also be done to it.     

三维新型非分裂场完全匹配层吸收边界条件

研究了一种3D新型时域有限差分法（FDTD）非分裂场近似完全匹配层（NPML）吸收边界。在直角坐标系中,通过直接对麦克斯韦方程组中的空间偏导的变量进行空间坐标拉伸,得到三维非分裂场的NPML吸收边界,这种吸收边界相对于PML吸收边界编程实现简单,编程复杂度低。通过对三维算例的电磁散射分析,验证了NPML吸收边界的正确性。计算结果表明了该方法是一个完美的吸收边界,可以用于实际目标的电磁散射问题分析。     

On the optimal design of the PML absorbing boundary condition forthe FDTD code

An analytical method to predict and optimize the performance of Berenger's (see J. Computat. Phys., vol.114, p.185-200, 1994) perfectly matched layer (PML) absorbing boundary condition (ABC) for finite-difference time-domain (FDTD) simulations is described. The shape of the conductivity in the PML layers has to be chosen carefully to obtain the best performance for a given number of layers. The relative error is shown to be the composite of two distinct effects: the theoretical reflection coefficient given by the PML layers backed by a metal plane and the second-order error in the differential intrinsic in the FDTD formulation. A theoretical expression to evaluate this error as a function of the number of PML layers and the shape of the conductivity is given, and the result is compared to that obtained for several FDTD test cases. The good agreement of the shapes of the theoretical and numerically derived curves allows the use of the theoretical formulation to optimize the PML region as a function of the shape of the conductivity, resolution, and number of layers     

A new technique for the quasi-TEM analysis of conductor-backedcoplanar waveguide structures

Numerically efficient and accurate formulae based on the spectral domain method for the analysis of conductor backed coplanar waveguide structures are presented. Quasi-TEM parameters are obtained for these waveguide structures by using piecewise linear functions to approximate the potential distribution at the air-dielectric interface. Techniques such as nonuniform discretization and bound estimation are described which demonstrate shorter computational times. Results on the characteristic impedance calculation of standard coplanar waveguide are given to demonstrate the numerical accuracy and efficiency of the method presented here     

A revised boundary condition for the numerical analysis of Schottky barrier diodes

A new boundary condition for the computer simulation of Schottky barrier diodes is proposed. In this model the electron transport analysis can be extended to higher bias voltages by utilizing a current-dependent surface recombination velocity which is based on a drifted Maxwellian distribution of carrier velocities. Calculations based on this revised boundary condition predict a depletion of electrons at the Schottky boundary compared with an accumulation predicted in previously published calculations.     

Photonic crystal waveguide analysis using interface boundary conditions

Devices based on combinations of photonic bandgap materials are understood intuitively in terms of the dispersion relations of the constituent periodic and locally homogeneous media. Quantitatively, though, photonic crystal-based devices are analyzed using numerical simulations which take no advantage of the a priori understanding of underlying periodic building-block materials. Here we unite the quantitative and qualitative pictures of photonic crystal devices and their design. We describe photonic crystals as effective media and impose boundary conditions between photonic crystals and homogeneous materials. We express optical field profiles as superpositions of plane waves in the homogeneous parts and propagating or decaying Bloch modes in the crystals, connected by transmission, reflection, and diffraction coefficients at the interfaces. We calculate waveguide modes, coupling lengths in directional couplers, and coupling between waveguides and point defects, achieving agreements of approximately 1% in frequencies and around 2% in quality factors. We use the new approach to optimize waveguide properties in a forward-going method, instead of the usual iterative optimizations.     

Second-order absorbing boundary conditions for marching-on-in-order scheme

In this letter, we derive second-order absorbing boundary conditions (ABCs) for a marching-on-in-order scheme, which is a time-domain method with weighted Laugerre polynomials and free of stability constraint. This method does not have to deal with time steps, and may be computationally much more efficient than conventional finite-difference time-domain (FDTD)methods with too many time steps to complete a solution. Starting from the three-dimensional (3-D) case of the marching-on-in-order scheme, we deduce a second-order ABC and apply it to a 3-D microstrip line example. The results show the second-order ABC performs better than the first-order one for guided wave problems.