A Two-Level Preconditioning Technique for Wire Antennas Attached with Dielectric Objects

An iterative solution of linear systems is studied,which arises from the discretization of a wire antennas attached with dielectric objects by the hybrid finite-element method and the method of moment (hybrid FEM-MoM).It is efficient to model such electromagnetic problems by hybrid FEM-MoM,since it takes both the advantages of FEM's and MoM's ability.But the resulted linear systems are complicated,and it is hard to be solved by Krylov subspace methods alone,so a two-level preconditioning technique will be studied and applied to accelerate the convergence rate of the Krylov subspace methods.Numerical results show the effectiveness of the proposed two-level preconditioning technique.     

Globally convergent iterative numerical schemes for nonlinearvariational image smoothing and segmentation on a multiprocessor machine

We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regularization methods from the image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than these stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multiprocessor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported     

A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.     

一种应用于目标宽带RCS快速计算的高效预处理技术

矩量法常与渐近波形估计技术结合用于目标宽带雷达散射截面的快速计算,然而当目标为电大尺寸时,此种方法仍然十分耗时。该文使用一种基于可变内外迭代技术的Krylov子空间迭代法FBICGSTAB求解由电场积分方程离散得到的大型稠密矩阵方程。同时近场矩阵预处理技术将与双阈值不完全LU分解预处理技术结合用于降低FBICGSTAB的迭代求解次数。数值计算表明:在不影响精度的前提下,该文方法可以大大提高目标宽带雷达散射截面的计算效率。     

A new iterative bidirectional beam propagation method

A new bidirectional beam propagation method is developed for numerical simulation of wave-guiding structures with multiple longitudinal reflecting interfaces. It is an iterative method that works on the wave field components directly. Operator rational approximations developed in the one-way beam propagation method are used together with a modern Krylov subspace iterative method. Compared with earlier bidirectional beam propagation methods based on the transfer matrix formulation, the new method is numerically stable and models evanescent modes better     

Model-order reduction by dominant subspace projection: error bound, subspace computation, and circuit applications

Balanced truncation is a well-known technique for model-order reduction with a known uniform reduction error bound. However, its practical application to large-scale problems is hampered by its cubic computational complexity. While model-order reduction by projection to approximate dominant subspaces without balancing has produced encouraging experimental results, the approximation error bound has not been fully analyzed. In this paper, a square-integral reduction error bound is derived for unbalanced dominant subspace projection by using a frequency-domain solution of the Lyapunov equation. Such an error bound is valid in both the frequency and time domains. Then, a dominant subspace computation scheme together with three Krylov subspace options is introduced. It is analytically justified that the Krylov subspace for moment matching at low frequencies is able to provide a better dominant subspace approximation than the Krylov subspace at high frequencies, while a rational Krylov subspace with a proper real shift parameter is capable of achieving superior approximation than the Krylov subspace at low frequency. A heuristic method of choosing a real shift parameter is also introduced based on its new connection to the discretization of a continuous-time model. The computation algorithm and theoretical analysis are then examined by several numerical examples to demonstrate the effectiveness. Finally, the dominant subspace computation scheme is applied to the model-order reduction of two large-scale interconnect circuit examples.     

Generalized Consistent Estimation on Low-Rank Krylov Subspaces of Arbitrarily High Dimension

The problem of Krylov subspace estimation based on the sample covariance matrix is addressed. The focus is on signal processing applications where the Krylov subspace is defined by the unknown second-order statistics of the observed samples and the signature vector associated with the desired parameter. In particular, the consistency of traditionally optimal sample estimators is revised and analytically characterized under a practically more relevant asymptotic regime, according to which not only the number of samples but also the observation dimension grow without bound at the same rate. Furthermore, an improved construction of a class of Krylov subspace estimators is proposed based on the generalized consistent estimation of a set of vector-valued power functions of the observation covariance matrix. To that effect, an extension of some known results from random matrix theory on the estimation of certain spectral functions of the covariance matrix to the convergence of not only the covariance eigenspectrum but also the associated eigensubspaces is provided. A new family of estimators is derived that generalizes conventional implementations by proving to be consistent for observations of arbitrarily high dimension. The proposed estimators are shown to outperform traditional constructions via the numerical evaluation of the solution to two fundamental problems in sensor array signal processing, namely the problem of estimating the power of an intended source and the estimation of the principal eigenspace and dominant eigenmodes of a structured covariance matrix.     

求解波导问题FEM线性系统的RIC预条件算法

提出了一种新型RIC预条件COCG迭代技术,用于改善有限元法仿真分析光电工程问题所产生的高度非正定的线性系统的迭代求解.提出的RIC预条件子是针对基本IC算法可能出现的分解崩溃问题,通过对主元进行加强来获得稳定的分解过程,进而产生高效的预条件子.数值试验表明,提出的RIC预条件子不仅能有效避免COCG迭代等方性崩溃,而且比常用的预条件子更高效;此外,RIC对其他若干Krylov子空间迭代法求解性能的改善作用也相当明显.     

Low-Cost Approximate LMMSE Equalizer Based on Krylov Subspace Methods for HSDPA

The throughput of the high speed downlink packet access (HSDPA) sub-system of UMTS suffers significantly from multiple access interference in the wireless channel. A linear minimum mean square error (LMMSE) equalizer at the receiver achieves higher throughput than a conventional RAKE receiver, at the cost of higher complexity. We introduce an iterative algorithm based on Krylov subspace projections, approximating the LMMSE equalizer with negligible loss of performance for the receiver. Slow variations of the channel can be exploited to allow further acceleration of the algorithm. Computational complexity as well as storage requirements are strongly reduced     

Robust Reduced-Rank Adaptive Algorithm Based on Parallel Subgradient Projection and Krylov Subspace

In this paper, we propose a novel reduced-rank adaptive filtering algorithm exploiting the Krylov subspace associated with estimates of certain statistics of input and output signals. We point out that, when the estimated statistics are erroneous (e.g., due to sudden changes of environments), the existing Krylov-subspace-based reduced-rank methods compute the point that minimizes a “wrong” mean-square error (MSE) in the subspace. The proposed algorithm exploits the set-theoretic adaptive filtering framework for tracking efficiently the optimal point in the sense of minimizing the “true” MSE in the subspace. Therefore, compared with the existing methods, the proposed algorithm is more suited to adaptive filtering applications. A convergence analysis of the algorithm is performed by extending the adaptive projected subgradient method (APSM). Numerical examples demonstrate that the proposed algorithm enjoys better tracking performance than the existing methods for system identification problems.      

A Spectral Multigrid Method Combined With MLFMM for Solving Electromagnetic Wave Scattering Problems

A new spectral multigrid method (SMG) combined with the multilevel fast multipole method (MLFMM) is proposed for solving electromagnetic wave scattering problems. The MLFMM is used to speed up the matrix-vector product operations and the SMG is employed to accelerate the convergence rate of the Krylov iteration. Unlike traditional algebraic multigrid methods (AMG), the spectral multigrid method is an algebraic two-grid cycle built on a preconditioned Krylov iterative method that is used as the smoother, and the grid transfer operators are defined using the spectral information of the preconditioned matrix. Numerical experiments indicate that this class of multigrid method is very effective with the MLFMM and can reduce both the iteration number and the overall simulation time significantly.     

一种低复杂度的信号子空间拟合的新方法

提出一种低复杂度的信号子空间拟合的新方法.证明了多级维纳滤波器的匹配滤波器(或降维矩阵的列矢量)可以张成一个压缩信号子空间.利用其与Krylov子空间等效这一特点,推导出信号子空间拟合一个新的基本公式,进而建立信号子空间拟合一个新的准则函数.分析表明,压缩信号子空间可以由降维矩阵的列矢量有效地张成,而且计算降维矩阵只需要多级维纳滤波器的若干步前向递推,所以本文方法的运算量和复杂度均较小.最后,计算机仿真验证了本文方法的有效性.     

一种新的阵元位置误差有源校正算法

阵列天线位置的不确定性会严重影响阵列天线的测向性能。文中基于子空间类测向方法,在远场情况下,提出了一种新的估计阵元位置误差的有源校正算法。该算法是以迭代的形式给出,其目标函数建立在信号子空间基本性质的基础上,适用于多个校正源同时存在的情况,并且可以应用于任意阵列形式。计算机仿真验证了文中的算法具有较快的收敛速度和较高的参数估计精度。     

线性迭代子空间射影重建法

该文提出了一种基于子空间线性迭代的射影重建方法,该方法利用所有的图像序列构成的行向量生成的线性子空间之和与射影重建结构点构成的行向量生成的子空间是同一线性子空间及在该子空间中任何一个基底都可以作为射影重建的特性,线性迭代地求取射影重建及图像深度因子。模拟实验和真实实验表明,该射影重建方法具有鲁棒性好、收敛性好及重投影误差小等优点。     

An adaptive extraction of generalized eigensubspace by using exact nested orthogonal complement structure

The contribution of this paper is three-fold: first, we propose a novel scheme for generalized minor subspace extraction by extending an idea of dimension reduction technique. The key of this scheme is the reduction of the problem for extracting the ith (i ≥ 2) minor generalized eigenvector of the original matrix pencil to that for extracting the first minor generalized eigenvector of a matrix pencil of lower dimensionality. The proposed scheme can employ any algorithm capable of estimating the first minor generalized eigenvector. Second, we propose a pair of such iterative algorithms and analyze their convergence properties in the general case where the generalized eigenvalues are not necessarily distinct. Third, by using these algorithms inductively, we present adaptive implementations of the proposed scheme for estimating an orthonormal basis of the generalized minor subspace. Numerical examples show that the proposed adaptive subspace extraction algorithms have better numerical stability than conventional algorithms.     

基于1维子空间线性迭代射影重建

提出了一种基于1维子空间线性迭代的射影重建方法.该方法利用所有图像序列的行向量生成的子空间之和,与射影重建空间点的行向量生成的子空间是同一线性子空间,同时,由第1幅图像的3个行向量及另外一个行向量可以构成该线性子空间的一个基底的特性,线性迭代求取这个行向量及图像深度因子,最后完成射影重建.模拟实验和真实实验数据结果表明,该射影重建方法具有鲁棒性好、收敛性好以及重投影误差小等优点.     

Nonlinear circuit-reduction of high-speed interconnect networksusing congruent transformation techniques

A new algorithm based on Krylov subspace methods is proposed for efficient simulation of large interconnect networks with nonlinear terminations. Reduction is obtained by projecting the original system described by nonlinear differential equations into a subspace of a lower dimension. The reduced circuit can be simulated using conventional numerical integration techniques. Significant reduction in computational expense is achieved as the size of the reduced equations is much less than that of the original system. The new algorithm is potentially useful for analysis of lossy coupled transmission lines with nonlinear terminations     

棱边元分区的区域分解算法及其在电磁问题中的应用

针对三维电磁问题,该文提出了采用非结构化网格剖分计算区域,并按单元进行区域划分的区域分解算法。将原求解区域划分为若干个不重叠的子区域,先通过求解容量矩阵获得子区域之间连接边界上的场值,再利用矢量有限元快速计算出每个子区域内部的场值,显著地降低了计算复杂度和存储量。通过引入预条件的Krylov子空间法求解容量矩阵方程,加速了收敛,进一步提高了效率。数值算例验证了该方法的准确性和有效性。     

Complexity Reduction of Iterative Receivers Using Low-Rank Equalization

This paper covers the consideration of an iterative or turbo receiver where the nonlinear trellis-based detection of the interleaved and coded data bits is replaced by linear detection using the Wiener filter (WF), i.e., the optimal linear filter based on the mean-square error (MSE) criterion. The equalization of channels with multiple antennas at the receiver as well as frequency-selective transfer functions requires high-dimensional observation vectors which involve computationally intense detectors. We extend an optimal but computationally efficient algorithm, originally derived for single receive antenna systems, to single-input multiple-output (SIMO) channels. To further reduce computational complexity, we apply the suboptimal low-rank multistage WF (MSWF), i.e., the WF approximation in the low-dimensional Krylov subspace, and replace additionally second-order statistics of nonstationary random processes by their time-invariant averages. Complexity investigations reveal the enormous capability of the proposed algorithms to decrease computational effort. Moreover, the analysis based on extrinsic information transfer (EXIT) charts as well as Monte Carlo simulations show that compared with reduced-rank detection methods based on eigensubspaces, the reduced-rank MSWF behaves near optimum although the rank is drastically reduced to two or even one     

Krylov subspace iterative techniques: on the detection of brain activity with electrical impedance tomography

In this paper, we review some numerical techniques based on the linear Krylov subspace iteration that can be used for the efficient calculation of the forward and the inverse electrical impedance tomography problems. Exploring their computational advantages in solving large-scale systems of equations, we specifically address their implementation in reconstructing localized impedance changes occurring within the human brain. If the conductivity of the head tissues is assumed to be real, the pre-conditioned conjugate gradients (PCGs) algorithm can be used to calculate efficiently the approximate forward solution to a given error tolerance. The performance and the regularizing properties of the PCG iteration for solving ill-conditioned systems of equations (PCGNs) is then explored, and a suitable preconditioning matrix is suggested in order to enhance its convergence rate. For image reconstruction, the nonlinear inverse problem is considered. Based on the Gauss-Newton method for solving nonlinear problems we have developed two algorithms that implement the PCGN iteration to calculate the linear step solution. Using an anatomically detailed model of the human head and a specific scalp electrode arrangement, images of a simulated impedance change inside brain's white matter have been reconstructed.