Rational approximants to the matrix exponential

The letter develops a method for obtaining a square matrix eNAt such that every element of eNAt is a proper rational function of t and is an efficient approximant to the corresponding element of the matrix exponential exp (At). Some useful general properties of eNAt are deduced and various procedures for computing eNAt are discussed.     

Analysis of the bounces on the power/ground plane structures byplanar circuit model and APA-E algorithm

In this paper, a novel effective numerical algorithm for analysis of the bounces on the power/ground-plane structure in printed circuit board (PCB) or multichip modules (MCMs) is proposed, which is based upon planar circuit model combined with APA-E algorithm. Firstly, the planar circuit model is developed to simulate the power/ground bounces when switching current is added in the structure. Secondly, on the basis of the abstract Pade approximant and the extrapolation algorithm, the APA-E algorithm is proposed. The classical multivariable rational Pade approximant is also constructed for comparison. Compared with finite difference time domain (FDTD) method, the new algorithm can provide a very accurate approximant in time domain, only requires little storage and CPU time. At last, attaching the decoupling capacitors for reducing the bounces on lossy power/ground-plane structures is also analyzed with this method     

Investigation of the Pade approximant-based wide-angle beampropagation method for accurate modeling of waveguiding circuits

An analytical and numerical study of the accuracy of the beam propagation method that includes approximate treatments of wide-angle propagation based on Pade rational functions is presented. The investigation identifies the error terms associated with a sequence of higher order operators and the range of validity of different approximant operators is studied through examination of two-dimensional (2-D) waveguide structures. An analytical model for the general error in Pade-based wide-angle schemes is developed and compared with numerical simulations of simple waveguiding devices for which the exact solution is known. Guidelines for determining the range of error pertinent to the Pade operator are established     

Pseudospectral beam-propagation method for optical waveguides

We propose a wide-angle pseudospectral beam-propagation method using the Pade approximant operator for strongly guiding and longitudinally varying optical waveguides. We validate the numerical results of our method by comparison against results obtained from a robust and widely used finite-element beam-propagation method.     

Inversion algorithm to construct Routh approximants

The purpose of the letter is to develop a direct method for deriving a kth-order Routh approximant, the main advantage being that, in order to find the parameters of a kth-order approximant, it will no longer be necessary to previously obtain those of all pth-order approximants (p?k?1), as occurs with the Hutton and Friedland method (1975).     

A finite-difference time-domain beam-propagation method for TE- and TM-wave analyses

The application of the existing time-domain beam-propagation method (TD-BPM) based on the finite-difference (FD) formula has been limited to the TE-mode analysis. To treat the TM mode as well as the TE mode, an improved TD-BPM is developed using a low-truncation-error FD formula with the aid of the alternating-direction implicit scheme. To improve the accuracy in time, a Pade (2,2) approximant is applied to the time axis. Although the truncation error in time is found to be O(/spl Delta/t/sup 2/), as in the case of the Pade (1,1) approximant, this method allows us to use a large time step. A substantial reduction in CPU time is found when compared to the conventional method in which a broadly banded matrix is solved by the Bi-CGSTAB. The effectiveness in evaluating the TE- and TM-mode waves is shown through the analysis of the power reflectivity from a waveguide facet. This method is also applied to the analysis of a waveguide grating. The accuracy and efficiency of the TD-BPM are assessed in comparison with the finite-difference time-domain method.     

回转激光位移传感器逼近式孔心定位方法

对于提高大型工件轴孔加工的精度和效率,孔心的精确定位至关重要。提出了一种基于激光位移传感器的非接触式回转逼近孔心定位方法。将传感器固定于机床的执行切削的旋转主轴上,并将主轴旋转中心置于理想圆心附近。在机床旋转的同时,分别沿与主轴轴线正交且相互垂直的两个方向上移动主轴,直到测量变化量达到最小(理论上可以为零),此时可以认为轴孔中心达到重合。利用逼近式孔心定位方法,可以快速精确定位与机床关联的圆心的相对坐标,从而指导后续加工。由于采用非接触测量方法,保障了测量的安全性。实验结果表明,此方法能够提高孔心的定位精度和效率。     

A stable bidirectional propagation method based on scatteringoperators

A stable bidirectional propagation method is developed based on the scattering operators and a complex coefficient Pade approximant to the square root operator. The method is then applied to a grating structure     

Remarks on system simplification using the Routh stability array

A novel method employing the Routh stability array is presented for obtaining a stable approximant for a stable system.     

Selection of the order of Routh approximants

A well known method for estimating in advance the order of a satisfactory Routh approximant does not always yield acceptable results. A simple criterion is thus proposed to check the results of this method.     

Electromagnetic scattering by rough conduction circular cylinders.I. Angular corrugation

The coherent and incoherent responses of perfectly conducting, angularly corrugated surfaces (which are infinite circular cylinders on the average) are calculated using a second-order perturbation method. The general approach used is to apply the extinction theorem to write an integral equation for the surface current density, and then to use perturbation theory to solve it. These results are recast by using the only nontrivial Pade approximant for this approximation. This recasting yield a considerable qualitative improvement which, at least in one special case, is shown to be quantitative as well     

Approximate scalar finite-element beam-propagation method withperfectly matched layers for anisotropic optical waveguides

The perfectly matched layer boundary condition for arbitrary anisotropic media is incorporated into the approximate scalar beam propagation method. The procedure is based on a finite-element method for three-dimensional anisotropic optical waveguides with off-diagonal elements in a permittivity tensor. In order to treat a wide-angle beam propagation, the Pade approximant operator is employed. To show the validity and usefulness of this approach, numerical results are presented for Gaussian beam propagation in free space and Gaussian beam excitation on a three-dimensional anisotropic optical waveguide     

Wide-angle propagating beam analysis for circularly symmetric waveguides: comparison between FD-BPM and FD-TDM

The finite-difference beam-propagation method (FD-BPM) with a (1, 1) Pade approximant operator is formulated for circularly symmetric waveguides. A tapered step-index fiber is analyzed, and the computed field distribution is compared with that from the scalar finite-difference time-domain method (FD-TDM). The present method offers improvement in the evaluation of a radiation-mode field compared with the conventional FD-BPM based on the paraxial approximation.     

An Arnoldi based thermal network reduction method for electro-thermal analysis

In this paper we consider the problem of approximating the large discretized thermal network that models the heat conduction phenomenon in an electrical system by means of models of reduced state-space dimensions. To this aim we present an efficient and numerically stable Arnoldi type algorithm by which a multi-point moment matching approximant of the discretized thermal network is obtained and we apply it to the electro-thermal analysis of an operational transconductance amplifier.     

Time-domain finite-difference BPM with Pade approximants in timeaxis for analysis of circularly symmetric fields

A Pade (2,2) approximant is applied to the time axis in the time-domain beam propagation method for circularly symmetric fields. By virtue of a multistep procedure, the Pade (2,2) operator is factored into a series of two Pade (1,1) operators. The present method offers substantial improvement in the analysis of pulse propagation. An upper limit of the time step is also discussed using the analysis of a fibre grating     

Finite element beam propagation method for anisotropic opticalwaveguides

A finite element beam propagation method (BPM) for anisotropic optical waveguides is newly formulated. In order to treat a wide-angle beam propagation, a Pade approximant operator is employed and to avoid nonphysical reflection from computational window edges, a transparent boundary condition is extended to anisotropic materials. To show the validity and usefulness of this approach, the numerical results for an anisotropic planar waveguide and a magnetooptic channel waveguide are presented     

统计推断约束下响应曲线的自适应Padé插值逼近

采用Pad啨插值技术 ,对计算获得的、稀疏的响应点值进行逼近 ,然后用获得的有理逼近式计算宽范围内响应曲线。把最小二乘法和插值技术结合起来 ,充分利用已有信息、达到最佳逼近的效果。同时自适应和精确地逼近响应曲线 ,引入了统计推断的办法。在统计推断的约束和判断下 ,实现了自适应的Pad啨插值逼近思煅榉椒ǖ恼沸?,应用了混合插值技术 ,对FDTD法计算获得的、稀疏的RCS频率和角度响应曲线进行了逼近 ,在统计推断办法的约束和判断下 ,获得了很好的效果     

A three-dimensional horizontally wide-angle noniterative beam-propagation method based on the alternating-direction implicit scheme

A three-dimensional horizontally wide-angle beam-propagation method is proposed on the basis of the alternating-direction implicit scheme, in which the Pade/spl acute/ approximant is applied only to the horizontal direction. The present formulation reduces the splitting error to the first order without an iteration procedure. The effectiveness is demonstrated through the wide-angle propagating beam analysis of a tilted optical waveguide.     

Combining the FDTD Method and Rational-Fitting Techniques for Modeling Active Devices Characterized by Measured S -Parameters

Most extensions of the original finite-difference time-domain (FDTD) method to incorporate lumped components are based on equivalent-circuit models. However, for active components, most manufacturers provide only the measured S-parameters of the device. This letter proposes the combination of the two-port lumped-network FDTD method and rational-fitting techniques to incorporate linear active devices characterized by measured 5-parameters into FDTD simulators. To this end, first the Y-parameters are obtained, which are then approximated by rational functions of the frequency over the band of interest. The polynomial coefficients resulting from the rational fitting are directly used to feed the FDTD simulation. The approach proposed here is applied to the calculation of the S-parameters of a microstrip amplifier. The results obtained are compared with those provided by the commercial simulator advanced design system and with measurements.     

A Stable Time-Domain Beam Propagation Method for Modeling Ultrashort Optical Pulses

A new technique to model ultrashort optical pulses is proposed and verified. The technique uses Pade approximant to account for the fast pulse propagational variations. Numerical parameters of the technique have been tested and it was shown that the method is simple, very stable, and accurate in modeling ultrashort optical pulses in long propagation interaction