Integral equations with reduced unknowns for the simulation oftwo-dimensional composite structures

A set of integral equations with reduced unknowns is derived for modeling two-dimensional inhomogeneous composite scatterers. The scatterer is first simulated in terms of thin curvilinear material layers of constant thickness. The traditional integral equations corresponding to each inhomogeneous layer are then manipulated in a manner allowing the identification of a new equivalent current component to replace two of the traditional ones across the layer. The given integral equations require approximately 2N current-component unknowns for their numerical implementation instead of the 3N unknowns generally required with traditional formulations. The implied computational efficiency though, was obtained at the expense of some complexity in the resulting pair of integral equations. To test the validity of the derived integral equations, special attention is given to a moment-method implementation of the authors' compact set of integral equations, with emphasis on the analytical evaluation of the diagonal and near-diagonal elements of the impedance matrix. Scattering patterns are presented as computed with the compact set of integral equations. These are further compared with measured data and computations using alternate analytical techniques. In all cases, these were in excellent agreement with corresponding results achieved by alternate methods     

Simultaneous thermal and electrical analysis of nonlinear microwavecircuits

A software tool for the simultaneous determination of the thermal and electrical steady-state regimes of nonlinear microwave circuits containing temperature-dependent active devices is introduced. The analysis technique is an extension of the classic piecewise harmonic-balance method, and is quite general-purpose. It can be applied to networks operating under multiple-tone excitation, including pulsed-RF regimes. The simulation problem is reduced to a nonlinear algebraic system whose unknowns are electrical and thermal state-variable harmonics. Advanced numerical techniques are used to overcome the difficulties arising from the high degree of nonlinearity and from the very large number of unknowns of the numerical problem. The program incorporates a facility for the evaluation of the thermal constants of multiple finger planar devices starting from geometrical data     

Macro-elements for efficient FEM simulation of small geometricfeatures in waveguide components

This paper introduces a novel class of specially constructed elements aimed at the expedient finite-element modeling of waveguide components containing fine geometric/material features such as dielectric and conducting posts. Instead of utilizing a very fine grid to resolve such fine features, special elements are constructed that capture accurately the electromagnetic properties of the fine features. Since the size of these macro-elements Is commensurate with the size of the elements of the grid used to discretize the volume in which the fine features are embedded, their use results in significant reduction in the number of unknowns in the finite-element approximation of the electromagnetic problem without sacrificing solution accuracy. The numerical implementation and effectiveness of the proposed macro-elements are demonstrated through several numerical experiments     

Relaxation procedure for phase retrieval of nonnegative signals

The paper presents an iterative procedure called the relaxation of autocorrelation equations (RAE) for solving the phase retrieval problem for nonnegative signals. First, the phase retrieval problem is formulated in the spatial domain as a set of polynomial equations with autocorrelations as known data and signal values as unknowns. Then, the RAE procedure solves these equations by recognizing one unknown at a time. While other unknowns are held constant at previously estimated values, a single unknown is varied inside the nonnegative region to globally minimize the sum of squared residuals of the equations with respect to the unknown. In every iteration, this procedure is repeated for each signal value. Since the sum of squared residuals is nonincreasing, the algorithm will either converge to a solution or stagnate; ways to overcome stagnation are suggested. The key feature of the RAE procedure is that unlike iterative transform algorithms, it allows direct control over bounding values of the signal at all times. Several numerical examples illustrate the RAE procedure     

Study of Algorithmic and Architectural Characteristics of Gaussian Particle Filters

In this paper, we analyze algorithmic and architectural characteristics of a class of particle filters known as Gaussian Particle Filters (GPFs). GPFs approximate the posterior density of the unknowns with a Gaussian distribution which limits the scope of their applications in comparison with the universally applied sample-importance resampling filters (SIRFs) but allows for their implementation without the classical resampling procedure. Since there is no need for resampling, we propose a modified GPF algorithm that is suitable for parallel hardware realization. Based on the new algorithm, we propose an efficient parallel and pipelined architecture for GPF that is superior to similar architectures for SIRF in the sense that it requires no memories for storing particles and it has very low amount of data exchange through the communication network. We analyze the GPF on the bearings-only tracking problem and the results are compared with results obtained by SIRF in terms of computational complexity, potential throughput, and hardware energy. We consider implementation on FPGAs and we perform detailed comparison of the GPF and SIRF algorithms implemented in different ways on this platform. GPFs that are implemented in parallel pipelined fashion on FPGAs can support higher sampling rates than SIRFs and as such they might be a more suitable candidate for real-time applications.     

The hybrid extended born approximation and CG-FFHT method foraxisymmetric media

The authors develop a hybrid implementation of the extended Born approximation (EBA) with the conjugate-gradient fast Fourier Hankel transform (CG-FFHT) method to improve the efficiency of the numerical solution of borehole induction problems in axisymmetric media. First, they use the FFHT to accelerate the EBA as a nonlinear approximation to induction problems, resulting in an algorithm with O(N log₂ N) arithmetic operations, where N is the number of unknowns in the problem. This accelerated EBA is accurate for most formations encountered in practical applications. Then, for formations with extremely high contrasts, they utilize the accelerated EBA as a partial preconditioner in the CG-FFHT method to solve the problem accurately with few iterations. The seamless combination of these two approaches provides an automatic way toward a general efficient and accurate modeling algorithm for induction measurements in axisymmetric media     

Diffraction of a plane wave by an inclined parallel plate grating

The diffraction of a plane electromagnetic wave by an inclined parallel plate grating is treated by using the Weiner-Hopf technique. The problem is formulated in terms of the single Wiener-Hopf equation, which is then using a factorization and decomposition procedure. The solution is exact but formal in the sense that there is an infinite number of unknowns. Approximation procedures are presented and two forms of the approximate solution are derived. Based on the above analysis, numerical examples are given and the transmission characteristics of the grating are discussed     

10 million unknowns: is it that big? [computational electromagnetics]

At the Center for Computational Electromagnetics at the University of Illinois, we recently solved a very-large-scale electromagnetic scattering problem. We computed the bistatic radar cross-section of a full-size aircraft at 8 GHz, involving the solution of a dense matrix equation with nearly 10.2 million unknowns. We regarded this as the "ultimate test" of a massively parallel implementation of the multilevel fast multipole algorithm (MLFMA), called ScaleME. In this paper, we narrate the technical difficulties faced and the experience gained from a very informal point of view. We describe the various methods developed for surmounting each of the obstacles.     

A robust integrated multibias parameter-extraction method forMESFET and HEMT models

An integrated multibias extraction technique for MESFET and high electron-mobility transistor (HEMT) models is presented in this paper. The technique uses S-parameters measured at various bias points in the active region to construct one optimization problem, of which the vector of unknowns contains a set of bias-dependent elements for each bias point and one set of bias-independent elements. This problem is solved by an extremely robust decomposition-based optimizer, which splits the problem into n subproblems, n being the number of unknowns. The optimizer consistently converges to the same solution from a wide range of randomly chosen starting values. No assumptions are made concerning the layout of the device or the bias dependencies of the intrinsic model elements. It is shown that there is a convergence in the values of the model elements and a decrease in the extraction uncertainty as the number of bias points in the extraction is increased. Robustness tests using 100 extractions, each using a different set of random starting values, are performed on measured S-parameters of a MESFET and pseudomorphic HEMT device. Results indicate that the extracted parameters typically vary by less than 1%. Extractions with up to 48 bias points were performed successfully, leading to the simultaneous determination of 342 model elements     

Method of moments enhancement technique for the analysis of Sierpinski pre-fractal antennas

The numerical analysis of highly iterated Sierpinski microstrip patch antennas by the method of moments (MoM) involves many tiny subdomain basis functions, resulting in a very large number of unknowns. The Sierpinski pre-fractal can be defined by an iterated function system (IFS). As a consequence, the geometry has a multilevel structure with many equal subdomains. This property, together with a multilevel matrix decomposition algorithm (MLMDA) implementation in which the MLMDA blocks are equal to the IFS generating shape, is used to reduce the computational cost of the frequency analysis of a Sierpinski based structure.     

Least-square-exponential approximation

A method is presented for solving the problem of fitting decay-type experimental data by sums of exponentials. Both the exponents and the coefficients of the exponentials are considered as unknowns. The novel idea presented here is to consider the sum of exponentials as a solution of an integral equation. A step-by-step procedure is given for the solution of the problem in the least-squares sense. An advantage of the proposed method is that the data need not be equidistant.     

正负交替反转法解析电子衍射相位问题

与X射线晶体学中存在的相位问题类似,在电子衍射中也存在相位问题:在电子衍射实验中只能收集到衍射强度而丢失了相位.最近,衍射重构成像方法(diffractive imaging),即直接从衍射重构出晶体结构的方法,从理论和实验都有了重大进展.从理论上,人们提出和发展许多有效的相位解析方法.从实验上,高强度的X射线源,场发射电子枪以及高灵敏度的记录媒介的发展都对此有贡献.直接从衍射重构出晶体结构有许多的优点:首先在重构像中,物镜球差的影响很小.这是由于物镜传递函数对衍射强度的影响远远小于对相位的影响;其次,从同一晶体收集的电子衍射有更多的高阶衍射斑,使得衍射重构能得到较高的分辨率(小于0.1 nm);同时,在同样辐射条件下晶体的电子衍射比其高分辨像具有更高的信噪比.这对于用电镜解析对辐射损伤敏感的有机物和生物蛋白晶体是有用的.本文叙述了一个解决电子衍射相位的新方法.在本文的程序中,同时使用了Oszlányi和Süto提出的正负交替反转法(charge-flipping algorithm)和Fienup的重构方法(hybrid input-output algorithm).作者用模拟数据来验证该方法的有效性.在程序中输入计算的运动学电子衍射强度,模拟晶体的二维静电势场分布能被重构出来.使用归一化结构因子可以提高正空间的重构像衬度;这对解决相位问题是有利的.使用Fienup的重构方法可以有效地解决由局域最小值而引起程序停滞问题.在正负交替反转法中通常会有停滞问题而不能找到全局最小值.正负交替反转法会逐步地在正空间中产生较大的零值电势区域,从而减小了正空间中未知数的数目.当未知数数目小于或等于从傅立叶变换建立起来的等式数目时,晶体的相位就可以解决了.     

Simultaneous wavelet estimation and deconvolution of reflectionseismic signals

The problem of simultaneous wavelet estimation and deconvolution is investigated with a Bayesian approach under the assumption that the reflectivity obeys a Bernoulli-Gaussian distribution. Unknown quantities, including the seismic wavelet, the reflection sequence, and the statistical parameters of reflection sequence and noise are all treated as realizations of random variables endowed with suitable prior distributions. Instead of deterministic procedures that can be quite computationally burdensome, a simple Monte Carlo method, called Gibbs sampler, is employed to produce random samples iteratively from the joint posterior distribution of the unknowns. Modifications are made in the Gibbs sampler to overcome the ambiguity problems inherent in seismic deconvolution. Simple averages of the random samples are used to approximate the minimum mean-squared error (MMSE) estimates of the unknowns. Numerical examples are given to demonstrate the performance of the method     

An integrated multiscaling strategy based on a particle swarm algorithm for inverse scattering problems

The application of a multiscale strategy integrated with a stochastic technique to the solution of nonlinear inverse scattering problems is presented. The approach allows the explicit and effective handling of many difficulties associated with such problems ranging from ill-conditioning to nonlinearity and false solutions drawback. The choice of a finite dimensional representation for the unknowns, due to the upper bound to the essential dimension of the data, is iteratively accomplished by means of an adaptive multiresolution model, which offers a considerable flexibility for the use of the information on the scattering domain acquired during the iterative steps of the multiscaling process. Even though a suitable representation of the unknowns could limit the local minima problem, the multiresolution strategy is integrated with a customized stochastic optimizer based on the behavior of a particle swarm, which prevents the solution from being trapped into false solutions without a large increasing of the overall computational burden. Selected examples concerned with a two-dimensional microwave imaging problem are presented for illustrating the key features of the integrated stochastic multiscaling strategy.     

Frequency response of 2-dimensional digital filters

A state-space representation of an elementary 2-dimensional digital network is presented. The problem of determining the frequency response starting from its state-space equation is reduced to solving two sets of linear simultaneous equations in real unknowns at each pair of frequencies. The efficiency and the computational aspects of the proposed method are also discussed.     

Electromagnetic and semiconductor device simulation usinginterpolating wavelets

A MESFET and a two-dimensional cavity enclosing a cylinder are simulated using a nonuniform mesh generated by an interpolating wavelet scheme. A self-adaptive mesh is implemented and controlled by the wavelet coefficient threshold. A fine mesh can therefore be used in domains where the unknown quantities are varying rapidly and a coarse mesh can be used where the unknowns are varying slowly. It is shown that good accuracy can be achieved while compressing the number of unknowns by 50% to 80% during the whole simulation. In the case of the MESFET, the I-V characteristics are obtained and the accuracy is compared with the basic finite difference scheme. A reduction of 83% in the number of discretization points at steady state is obtained with 3% error on the drain current. The performance of the scheme is investigated using different values of threshold and two types of interpolating wavelet, namely, the second-order and fourth-order wavelets. Due to the specific problem analyzed, a tradeoff appears between good compression, accuracy, and order of the wavelet. This represents the ongoing effort toward a numerical technique that uses wavelets to solve both Maxwell's equations and the semiconductor equations. Such a method is of great interest to deal with the multiscale problem that is the full-wave simulation of active microwave circuits     

Wire antennas in the presence of a dielectric/ferrite inhomogeneity

A moment method solution for treating thin-wire antennas in the presence of an arbitrary dielectric and/or ferrite inhomogeneity is presented. The wire is modeled by an equivalent surface current density, and the dielectric/ferrite inhomogeneity is modeled by equivalent volume polarization currents. The conduction currents on the wire and the polarization currents in the dielectric/ferrite inhomogeneity are treated as independent unknowns and determined in the moment method solution. The method is applied to the problem of a loop antenna loaded with dielectric or ferrite. Numerical results are presented, and are in good agreement with measurements and previous calculations.     

An `add-on' method for the analysis of scattering from large planarstructures

A so-called add-on procedure is proposed to deal with the data analysis problem resulting from the collection of scattering data from large planar structures. The computations (involving of the order of a few thousand unknowns) is undertaken in a gradual manner by building up the body from small patches which are added sequentially. The procedure is based on an initial expansion of the unknown current distribution into subsectional (pulse-type) basic functions. Each segment of the scatterer carries an unknown amplitude which is the response to an incident wave. However, rather than forming a matrix equation for these responses, they are computed in a gradual manner where the scatterer is built up from these segments as they are added one at a time. At the end of each addition of a segment, the result for scattering from a partial body is obtained. At each stage, the problem solved reflects the size of the small addition only, and the solution to an actual partial body is obtained. An important feature of this method is its ability to utilize a priori known information on a portion of the scatterer as an initial stage for the economic analysis of the entire structure. The process takes into account the interactions between all segments of the body. The process proves to be very efficient both in terms of computation time and storage requirements, as seen in the computed examples on of the order of 1000 to 6000 unknowns     

A boundary element approach to the scattering from inhomogeneousdielectric bodies

A boundary element method (BEM) for the analysis of the electromagnetic scattering from inhomogeneous dielectric structures is presented. The problem is formulated in terms of a single integral equation reducing by half the number of unknowns required with respect to a conventional approach based on two coupled integral equations