Sparse inverse preconditioning of multilevel fast multipole algorithm for hybrid Integral equations in electromagnetics

In computational electromagnetics, the multilevel fast multipole algorithm (MLFMA) is used to reduce the computational complexity of the matrix vector product operations. In iteratively solving the dense linear systems arising from discretized hybrid integral equations, the sparse approximate inverse (SAI) preconditioning technique is employed to accelerate the convergence rate of the Krylov iterations. We show that a good quality SAI preconditioner can be constructed by using the near part matrix numerically generated in the MLFMA. The main purpose of this study is to show that this class of the SAI preconditioners are effective with the MLFMA and can reduce the number of Krylov iterations substantially. Our experimental results indicate that the SAI preconditioned MLFMA maintains the computational complexity of the MLFMA, but converges a lot faster, thus effectively reduces the overall simulation time.     

基于分解和超平面拟合的进化超多目标优化降维算法

目标降维是研究超多目标优化问题的一个重要方向,它通过恰当的算法设计,能够剔除一些对求解优化问题冗余的目标,达到极大简化优化问题的效果。在超多目标优化降维问题中,前沿界面呈现非线性的情形是最普遍也是最难处理的降维问题。该文提出一种基于分解和超平面拟合的算法(DHA)来处理这类目标降维问题,通过对进化过程中种群的有效分解,使得在几何上非线性分布的非劣解集近似分解为多个近似线性分布的子集,再用系数是稀疏的超平面结合一些扰动项去拟合这些非劣解子集,最后根据该超平面提取出原问题的本质目标集,达到去除冗余目标的效果。为了检验提出算法的有效性,采用DTLZ5(I, m), WFG3(I, m)和MAOP(I, m)作为测试问题集,与代表当今水平的著名算法进行比较。计算机仿真结果表明该文提出的算法无论前沿界面是线性或非线性的情形都具有优异的性能。     

A spectral Lanczos decomposition method for solving 3-Dlow-frequency electromagnetic diffusion by the finite-elementmethod

A very efficient three-dimensional (3-D) solver for the diffusion of the electromagnetic fields in an inhomogeneous medium is described. The proposed method employs either the node-based or the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution in the frequency domain. By analyzing some practical geophysical problems, it is shown that the SLDM is extremely fast and, furthermore, the electromagnetic fields at many frequencies can be evaluated by performing the SLDM iteration only at the lowest frequency     

时分MIMO滑坡雷达稀疏成像算法

针对现用于成像的MIMO山体滑坡雷达均匀线性阵列数目过多、数据处理复杂度高的问题，引入稀疏阵列时分地基MIMO雷达模型，提出一种基于逆傅里叶变换和混合匹配追踪算法的成像方法。首先通过对雷达回波信号作逆傅里叶变换实现距离向压缩，并进行近似相位补偿，然后采用一种基于时延补偿因子稀疏基的压缩感知算法实现方位向压缩。同时针对多目标成像的伪影点问题，方位向数据压缩引入子空间追踪算法和正交匹配追踪算法的结合算法重构出高分辨率且没有伪影的二维图像。根据真实的山体滑坡监测成像场景参数，通过数值仿真验证了该方法能够在低于传统均匀阵列的天线数目情况下实现目标高质量成像，且具有一定的抗噪性。     

Modeling multiple IP traffic streams with rate limits

We start with the premise, and provide evidence that it is valid, that a Markov-modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the parameters and size of a discrete MMPP (D-MMPP) from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the MMPP describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that are not tandem, we show how to approximate the superposition of MMPPs without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated D-MMPP to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model.     

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.     

Application of subspace projection approaches for reduced-order modeling of electromagnetic systems

Subspace projection approaches, including the Pade/spl acute/ via Lanczos (PVL), Krylov, and rational Krylov algorithms, are used for reduced-order modeling of wide-band electromagnetic systems. The properties of these algorithms are discussed. A frequency segmentation technique has also been used with the Lanczos algorithm to obtain benchmark data of electromagnetic fields and for scattering parameter extraction from the calculated electromagnetic field values. From the various techniques, the combined PVL/frequency segmentation technique is the most promising for efficient and accurate modeling of electromagnetic systems.     

Analysis of Packet Network Congestion Control Using Sparse Matrix Algorithms

The purpose of this study is twofold. First the study illustrates the utility of applying sparse matrix methods to packet network models. Secondly, these methods are used to give new results about the control of store and forward congestion in packet networks. Store and forward congestion (node to node blocking) reduces the effective traffic carrying capacity of the network by unnecessarily idling network resources. This study shows how store and forward congestion can be controlled by a combination of buffer reservation and processor capacity allocation. The scheme presented is analyzed using a Markovian state-space model of two coupled packet switches. The model contains more detail than previous analytic models. It is therefore solved using numerical sparse matrix methods. The results show that the combination of buffer reservation and processor capacity allocation gives strictly nondecreasing network output as a function of increasing network input load, i.e., undesirable store and forward congestion effects are eliminated.     

模型噪声中的稀疏恢复算法研究

针对观测和传感矩阵都存在噪声扰动的欠定线性系统的稀疏恢复问题,该文基于FOCUSS(FOCal Underdetermined System Solver)算法提出了一种改进算法SD(Synchronous Descending)-FOCUSS。文中由MAP(最大后验)估计方法推导出系统模型的的目标函数,应用松弛迭代算法对其进行优化从而找到近似最优的稀疏解。SD-FOCUSS算法可应用于MMV(多观测向量)模型。可证明SD-FOCUSS是收敛算法;最后用仿真实验展示了与其他算法相比时,新算法在准确性、稳定性等方面的优越性。     

A new finite element model for reduced order electromagneticmodeling

This paper introduces a new formulation suitable for direct model order reduction of finite element approximations of electromagnetic systems using Krylov subspace methods. The proposed formulation utilizes a finite element model of Maxwell's curl equations to generate a state-space representation of the electromagnetic system most suitable for the implementation of model order reduction techniques based on Krylov subspaces. It is shown that, with a proper selection of the finite element interpolation functions for the fields, the proposed formulation is equivalent to the commonly used approximation of the vector wave equation with tangentially continuous vector finite elements. This equivalence is exploited to improve the computational efficiency of the model order reduction process     

A Krylov Subspace Method for Covariance Approximation and Simulation of Random Processes and Fields

This paper proposes a new iterative algorithm for simultaneously computing an approximation to the covariance matrix of a random vector and drawing a sample from that approximation. The algorithm is especially suited to cases for which the elements of the random vector are samples of a stochastic process or random field. The proposed algorithm has close connections to the conjugate gradient method for solving linear systems of equations. A comparison is made between our algorithm's structure and complexity and other methods for simulation and covariance matrix approximation, including those based on FFTs and Lanczos methods. The convergence of our iterative algorithm is analyzed both analytically and empirically, and a preconditioning technique for accelerating convergence is explored. The numerical examples include a fractional Brownian motion and a random field with the spherical covariance used in geostatistics.     

Efficient time-domain and frequency-domain finite-element solutionof Maxwell's equations using spectral Lanczos decomposition method

An efficient three-dimensional solver for the solution of the electromagnetic fields in both time and frequency domains is described. The proposed method employs the edge-based finite-element method (FEM) to discretize Maxwell's equations. The resultant matrix equation after applying the mass-lumping procedure is solved by the spectral Lanczos decomposition method (SLDM), which is based on the Krylov subspace (Lanczos) approximation of the solution. This technique is, therefore, an implicit unconditionally stable finite-element time and frequency-domain scheme, which requires the implementation of the Lanczos process only at the largest time or frequency of interest. Consequently, a multiple time- and frequency-domain analysis of the electromagnetic fields is achieved in a negligible amount of extra computing time. The efficiency and effectiveness of this new technique are illustrated by using numerical examples of three-dimensional cavity resonators     

ICCAP-a linear time sparsification and reordering algorithm for 3-D BEM capacitance extraction

This paper presents an efficient, simple, hierarchical, and sparse three-dimensional capacitance extraction algorithm, i.e., ICCAP. Most previous capacitance extraction algorithms, such as FastCap and HiCap, introduce intermediate variables to facilitate the hierarchical potential calculation, but still preserve the basic panels as basis. In this paper, we discover that those intermediate variables are a fundamentally much better basis than leaf panels. As a result, we are able to explicitly construct the sparse potential coefficient matrix and solve it with linear memory and linear run time in comparison with the most recent hierarchical O(nlogn) approach in PHiCap. Furthermore, the explicit sparse formulation of a potential matrix not only enables the usage of preconditioned Krylov subspace iterative methods, but also the reordering technique. A new reordering technique, i.e., level-oriented reordering (LOR), is proposed to further reduce over 20% of memory consumption and run time compared with no reordering techniques applied. In fact, LOR is even better than the state-of-the-art minimum degree reordering and more efficient. Without complicated orthonormalization matrix computation, ICCAP is very simple, efficient, and accurate. Experimental results demonstrate the superior run time and memory consumption over previous approaches while achieving similar accuracy.     

Semivectorial Helmholtz beam propagation by Lanczos reduction

By using the finite-difference method to perform Lanczos reduction, a semivectorial Helmholtz beam propagation algorithm is demonstrated. The applicability of this algorithm is no longer limited to paraxial beams and scalar fields. Mode indices of rib waveguides are calculated and compared to previously published data. Losses of Y -branch for two orthogonal polarizations are also presented. This algorithm is more efficient than the conventional beam propagation method in determining the mode index. To calculate the radiation loss however, it requires much more computational effort. More than 30 Krylov vectors are needed to avoid numerical dissipation     

Analysis of frequency selective surfaces through the blazing onsetusing rational Krylov model-order reduction and Woodbury singularityextraction

Rational Krylov model-order reduction techniques are used to accelerate the characterization of frequency selective surfaces (FSSs) over broad spectral ranges, including frequencies at which a higher order Floquet mode stops evanescing and begins to propagate. The procedure comprises three main stages: (1) construction of the spectral Galerkin system at a small set of frequencies, (2) linearization of that system, and (3) reduction of the linearized system using the rational Krylov technique. The inclusion of blazing frequencies in the band of interest complicates the second and third of these steps because of the branch point singularity in the periodic Green's function. This difficulty is avoided by removing the blazing modes contributions to the spectral Galerkin matrix using the Woodbury formula for low-rank updates. The algorithm results in a set of small linear systems producing outputs that are combined to approximate the reflection and transmission coefficients of all propagating modes. The technique is applied to three different frequency selective surfaces and is shown to be accurate and efficient in all cases     

A new approach to rapid PN code acquisition using iterative message passing techniques

Iterative message passing algorithms on graphs, which are generalized from the well-known turbo decoding algorithm, have been studied intensively in recent years because they can provide near-optimal performance and significant complexity reduction. In this paper, we demonstrate that this technique can be applied to pseudorandom code acquisition problems as well. To do this, we represent good pseudonoise (PN) patterns using sparse graphical models, then apply the standard iterative message passing algorithms over these graphs to approximate maximum-likelihood synchronization. Simulation results show that the proposed algorithm achieves better performance than both serial and hybrid search strategies in that it works at low signal-to-noise ratios and is much faster. Compared with full parallel search, this approach typically provides significant complexity reduction.     

一种基于拟牛顿法的CS投影矩阵优化算法

压缩感知(Compressed Sensing,CS)理论中,投影矩阵优化是一类通过提高观测数据信息量而改善性能的方法.由于投影矩阵与稀疏字典内积构造的Gram矩阵必定奇异,基于广义逆矩阵求解方法存在计算精度的问题.本文提出了一种利用拟牛顿法的CS投影矩阵优化算法.该算法分为两步:一是利用阈值函数约束Gram矩阵非对角线元素,使投影矩阵与稀疏字典的互相关系数逼近Welch界;二是采用秩2校正得到Hessian阵逆近似去修正梯度搜索方向.两个步骤交替执行,直到解出符合优化要求的投影矩阵.该算法始终保持下降性,具有超线性收敛速度,避免了矩阵函数二阶导数复杂的计算,计算量较小.实验结果表明,当信号稀疏度或观测数据相同时,本文算法的重构结果优于其他算法.     

Architecture-Level Thermal Characterization for Multicore Microprocessors

This paper investigates a new architecture-level thermal characterization problem from a behavioral modeling perspective to address the emerging thermal related analysis and optimization problems for high-performance multicore microprocessor design. We propose a new approach, called ThermPOF, to build the thermal behavioral models from the measured or simulated thermal and power information at the architecture level. ThermPOF first builds the behavioral thermal model using the generalized pencil-of-function (GPOF) method. Owing to the unique characteristics of transient temperature changes at the chip level, we propose two new schemes to improve the GPOF. First, we apply a logarithmic-scale sampling scheme instead of the traditional linear sampling to better capture the temperature changing behaviors. Second, we modify the extracted thermal impulse response such that the extracted poles from GPOF are guaranteed to be stable without accuracy loss. To further reduce the model size, a Krylov subspace-based reduction method is performed to reduce the order of the models in the state-space form. Experimental results on a real quad-core microprocessor show that generated thermal behavioral models match the given temperature very well.     

未知信源数目的DOA估计方法

针对信源数目未知情况下的DOA估计问题,该文提出了两种基于稀疏表示的DOA估计方法。一种是基于阵列协方差矩阵特征向量稀疏表示的DOA估计方法,首先证明了阵列协方差矩阵的最大特征向量是所有信号导向矢量的线性组合,然后利用阵列协方差矩阵的最大特征向量建立稀疏模型进行DOA估计;另一种是基于阵列协方差矩阵高阶幂稀疏表示的DOA估计方法,根据信号特征值大于噪声特征值的特性,通过对协方差矩阵的高阶幂逼近信号子空间,利用协方差矩阵的高阶幂的列向量建立DOA估计的稀疏模型进行DOA估计。理论分析和仿真实验验证,两种方法都不需要进行信号源数目的估计,具有较高的精度、较好的分辨力,对相干信号也具有优越的适应能力。