Algebraic multigrid preconditioner for homogeneous scatterers in electromagnetics

Electromagnetic wave scattering from large and complex bodies is currently the most challenging problem in computational electromagnetics. There is an increasing need for more efficient algorithms with reduced computational complexity and memory requirements. In this work we solve the problem of electromagnetic wave scattering involving three-dimensional, homogeneous, arbitrarily shaped dielectric objects. The fast multipole method (FMM) is used along with the algebraic multigrid (AMG) method, that is employed as a preconditioner, in order to accelerate the convergence rate of the Krylov iterations. Our experimental results suggest much faster convergence compared to the non preconditioned FMM, and hence significant reduction to the overall computation time.     

快速多极子在任意截面均匀介质柱散射中的应用

采用快速多极子法（FMM）加速后的矩量法（MoM）求解由电磁场等效原理导出的关于均匀介质柱表面等铲电磁流的积分方程,进而计算其电磁散射特性,FMM的引入使计算时间和内存开销都从O(N^2）降到O（N^3/2）,且并不增加多少复杂度。最后给出了一些介质柱体RCS的算例。     

Genetic algorithms for finite mixture model based voxel classification in neuroimaging

Finite mixture models (FMMs) are an indispensable tool for unsupervised classification in brain imaging. Fitting an FMM to the data leads to a complex optimization problem. This optimization problem is difficult to solve by standard local optimization methods, such as the expectation-maximization (EM) algorithm, if a principled initialization is not available. In this paper, we propose a new global optimization algorithm for the FMM parameter estimation problem, which is based on real coded genetic algorithms. Our specific contributions are two-fold: 1) we propose to use blended crossover in order to reduce the premature convergence problem to its minimum and 2) we introduce a completely new permutation operator specifically meant for the FMM parameter estimation. In addition to improving the optimization results, the permutation operator allows for imposing biologically meaningful constraints to the FMM parameter values. We also introduce a hybrid of the genetic algorithm and the EM algorithm for efficient solution of multidimensional FMM fitting problems. We compare our algorithm to the self-annealing EM-algorithm and a standard real coded genetic algorithm with the voxel classification tasks within the brain imaging. The algorithms are tested on synthetic data as well as real three-dimensional image data from human magnetic resonance imaging, positron emission tomography, and mouse brain MRI. The tissue classification results by our method are shown to be consistently more reliable and accurate than with the competing parameter estimation methods.     

压缩感知结合FMM分析目标宽角度电磁散射问题

应用快速多极子方法(FMM)直接计算宽角度电磁散射问题时,需要对每一个入射角度迭代求解,计算量较大,效率较低。基于快速多极子方法中聚合、转移和发散过程与电磁波入射方向的无关性,将压缩感知理论(CS)引入并构建富含空间信息的新型激励源,仅由远小于入射角度数目的几次快速多极子计算,即可获得感应电流的观测值,近而恢复出所有入射角度下的激励电流。与传统矩量法结合压缩感知理论方法相比,该方法的计算精度较高,并且计算时间大幅减少。     

Acceleration of Fast Multipole Method for Large-Scale Periodic Structures With Finite Sizes Using Sub-Entire-Domain Basis Functions

An acceleration technique to the fast multipole method (FMM) has been proposed to handle large-scale problems of periodic structures in free space with finite sizes based on the accurate sub-entire-domain basis functions. In the proposed algorithm, only nine (or 27) elements in the whole impedance matrix are required to be computed and stored for a two-dimensional (or three-dimensional) periodic structure, and the matrix-vector multiply can be performed efficiently using the combination of fast Fourier transform and FMM. The theoretical analysis and numerical results show that both the memory requirement and computational complexity are only of the order of O(N) with small constants, where N is the total number of unknowns     

Parallel in-core and out-of-core solution of electrically large problems using the RWG basis functions

Currently, the problem size that can be solved in reasonable time using the Method of Moments is limited by the amount of memory installed in the computer. This paper offers a new development that not only breaks this memory constraint, but also maintains the efficiency of running the problem in-core. In this paper, highly efficient parallel matrix-filling schemes are presented for parallel in-core and parallel out-of-core integral-equation solvers with subdomain RWG basis functions. The parallel methodology for matrix filling is quite different when using a subdomain basis as opposed to using a higher-order basis. The parallel in-core solver uses memory, which is often expensive and limited in size. The parallel out-of-core solver is introduced to extend the capability of MoM to solve larger problems that can be as large as the amount of storage on the hard disk. Numerical results on several typical computer platforms show that the parallel matrix-filling schemes and matrix-equation solvers introduced here are highly efficient and achieve theoretical predictions. The implementation of these advancements with the widely used RWG basis functions creates a powerful tool for efficient computational electromagnetics solution of complex real-world problems.     

FMM用于快速计算电大腔体的RCS

利用迭代物理光学法(IPO)计算一般电大尺寸腔体的电磁散射特性,在迭代过程中用快速多极子方法(FMM)加速计算.在雅可比最小残差法(JMRES)的积分运算中引入FMM并与共扼梯度法(CG)的计算效率进行了比较.采用结构化分组,利用转移因子的平移不变性对计算和存储进行了优化.计算结果表明这些加速方法是有效的并能极大地提高计算效率.     

Multitarget state and track estimation for the probability hypotheses density filter

The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the estimates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) approaches are used for the FMM parameter estimation.     

A fast multipole-method-based calculation of the capacitance matrixfor multiple conductors above stratified dielectric media

An efficient static fast-multipole-method (FMM)-based algorithm is presented in this paper for the evaluation of the parasitic capacitance of three-dimensional microstrip signal lines above stratified dielectric media. The effect of dielectric interfaces on the capacitance matrix is included in the stage of FMM when outgoing multipole expansions are used to form local multipole expansions by the use of interpolated image outgoing-to-local multipole translation functions. The increase in computation time and memory usage, compared to the free-space case, is, therefore, small. The algorithm retains O(N) computational and memory complexity of the free-space FMM, where N is the number of conductor patches     

并行FDTD和IBM BlueGene/L巨型计算机结合求解电大尺寸的电磁问题

高性能巨型计算机的快速发展正在改变着人们在计算电磁学方面的一些传统观念,特别是IBM BlueGene/L巨型计算机的出现使计算电磁学所解决的问题尺寸和时间发生了巨大的变化.IBM BlueGene/L巨型计算机可以包括多达65,536处理器和 32 TB 内存,更重要的是由于它所使用的特殊体系结构使它在4000个处理器时时域有限差分程序的并行效率仍然在百分之九十左右.测试显示,在单个CPU速度接近的情况下,一台奔腾4计算机上运行五十二天的工作量在一个包含有4000个处理器的BlueGene/L巨型计算机上仅需10min左右.虽然普通的PC机群与单个处理器相比也能快速地求解相对大的问题,但是无论是使用千兆 Ethernet、Foundry、Myrinet或者Infiniband,普通PC机群的效率都会在处理其数量超过几十个的时候快速下降.为了验证并行时有预先差分程序的正确性,我们使用并行时域有限差分程序在巨型计算机IBM BlueGene/L上模拟一个144单元的对偶极化Vivaldi阵列的抛物面天线馈源.     

三维电磁波体积分方程的快速多极子算法

该文提出用快速多极子方法(FMM)求解三维非均匀介质散射体的电磁散射,将以往边界方程的FMM推广到三维矢量电磁波体积分方程(3DV-FMM),推导了一级和多级快速多极子的三维体积分离散公式。这一方法减少了计算机存储要求,并从量级上降低了共轭梯度迭代求解的矩量法的计算量。在计算中,选用函数作基函数,达到相当好的收敛性．本文用3DV-FMM数值计算了三维均匀和非均匀介质立方体,多个介质体的双站散射截面(RCS),以及任一剖面上的等效电流体密度分布。计算结果与矩量法相吻合,但在计算内存和CPU时间上要节省得多。本文的方法也可为三维电磁波逆散射的反演算法研究给出正向模拟的快速计算。     

一种适合FMM法的预处理技术在车载通信系统中的应用

提出了一种针对适合于快速多极子(FMM)近场作用矩阵的不完全LU预条件方法。与传统单纯靠填充参数来控制非零元素个数的ILU分解方法相比,该方法由于引入了数值丢弃阈值,因而可以获得更好的预条件矩阵。利用该预条件技术,收敛更快,计算花费的时间和存储量更少。数值试验表明,此方法是一种适合FMM计算的预条件技术。     

Parallelization of the EM algorithm for 3-D PET image reconstruction

The EM algorithm for PET image reconstruction has two major drawbacks that have impeded the routine use of the EM algorithm: the long computation time due to slow convergence and a large memory required for the image, projection, and probability matrix. An attempt is made to solve these two problems by parallelizing the EM algorithm on multiprocessor systems. An efficient data and task partitioning scheme, called partition-by-box, based on the message passing model is proposed. The partition-by-box scheme and its modified version have been implemented on a message passing system, Intel iPSC/2, and a shared memory system, BBN Butterfly GP1000. The implementation results show that, for the partition-by-box scheme, a message passing system of complete binary tree interconnection with fixed connectivity of three at each node can have similar performance to that with the hypercube topology, which has a connectivity of log(2) N for N PEs. It is shown that the EM algorithm can be efficiently parallelized using the (modified) partition-by-box scheme with the message passing model.     

用于复杂目标三维矢量散射分析的快速多极子方法

本文着重介绍了一种用于复杂目标三维电磁散射精确建模和数值分析的高型高效数值方法,即快速多极子方法和多层快速多极子方法。     

一种新型针对快速多极子法(FMM)的预条件技术

提出了一种针对FMM近场作用矩阵块的不完全LU预条件方法。和传统单纯依靠填充参数来控制非零元素个数的ILU分解方法相比，该方法由于引入了数值丢弃阈值，因而可获得性能更好的预条件矩阵。利用该项预条件技术，迭代过程变得更健壮，而且收敛也更快，计算花费的时间也更少。数值实验表明：这种基于双丢弃准则的ILUT预条件技术，是一种非常适合FMM计算的预条件处理方法。     

An IE-ODDM-MLFMA Scheme With DILU Preconditioner for Analysis of Electromagnetic Scattering From Large Complex Objects

For electrically large complex electromagnetic (EM) scattering problems, huge memory is often required for most EM solvers, which is too difficult to be handled by a personal computer (PC) even a workstation. Although the multilevel fast multipole algorithm (MLFMA) effectively deals with electrically large problems to some extent, it is still time and memory consuming for very large objects. In order to further reduce the CPU time and the memory requirement, a hybrid algorithm, based on the overlapped domain decomposition method for integral equations (IE-ODDM), MLFMA and block-diagonal, incomplete lower and upper triangular matrices (DILU) preconditioner, is proposed for the analysis of electrically large problems. The dominant memory requirement for plane wave expansions in the three processes of aggregation, translation and disaggregation in the MLFMA is drastically reduced by the first two techniques. The iterative procedure for each overlapped subdomain solved by the MLFMA is effectively sped up by the DILU preconditioner. After integrating these techniques, the proposed hybrid algorithm is more efficient in computing time and memory requirement compared to the conventional MLFMA and is more suitable for analyzing very large EM scattering problems. Enough accurate solution can be obtained within quite a few outer iterations, where an outer iteration means a complete sweep for all the subdomains. Some numerical examples are presented to demonstrate its validity and efficiency.     

Time discretization of continuous-time filters and smoothers forHMM parameter estimation

In this paper we propose algorithms for parameter estimation of fast-sampled homogeneous Markov chains observed in white Gaussian noise. Our algorithms are obtained by the robust discretization of stochastic differential equations involved in the estimation of continuous-time hidden Markov models (HMM's) via the EM algorithm. We present two algorithms: the first is based on the robust discretization of continuous-time filters that were recently obtained by Elliott to estimate quantities used in the EM algorithm; the second is based on the discretization of continuous-time smoothers, yielding essentially the well-known Baum-Welch re-estimation equations. The smoothing formulas for continuous-time HMM's are new, and their derivation involves two-sided stochastic integrals. The choice of discretization results in equations which are identical to those obtained by deriving the results directly in discrete time. The filter-based EM algorithm has negligible memory requirements; indeed, independent of the number of observations. In comparison the smoother-based discrete-time EM algorithm requires the use of the forward-backward algorithm, which is a fixed-interval smoothing algorithm and has memory requirements proportional to the number of observations. On the other hand, the computational complexity of the filter-based EM algorithm is greater than that of the smoother-based scheme. However, the filters may be suitable for parallel implementation. Using computer simulations we compare the smoother-based and filter-based EM algorithms for HMM estimation. We provide also estimates for the discretization error     

P(MoM/MAS): an interactive environment, coupling WWW technology andparallel processing, to solve large-size electromagnetic problems

Parallel processing over the Internet is now becoming a realistic possibility. There are numerous of-the-shelf high-performance computing (HPC) platforms available with Internet access, on which to implement computationally intensive algorithms. HPC can be applied in the field of computational electromagnetics. The networking capabilities of the Internet now allow these computing resources to be used as a remote service. Additionally, the pragmatics of their utilization can be abstracted by adopting a World Wide Web (WWW) interface. A Web-based environment can provide the supportive tools for data entry, program initiation, result visualization, and even interactive modifications of the geometry and/or electromagnetic (EM) properties. For realistic interaction, the emerging question is which algorithm to use that supports the exploitation of parallelism. In order to exploit and utilize all the available performance of current and predicted HPC platforms, inherently-parallel-based algorithms have to be devised. One such algorithm is the parallel method of moments/method of auxiliary sources, P(MoM/MAS), introduced in this paper. The resulting algorithm parallelization enables the MoM/MAS method to be applied to solving electrically-large-in-size and complex EM structures on various computational platforms. This paper concentrates on the parallel-processing issues, and on the importance of adopting suitable algorithms, such as the MoM/MAS technique     

MoM-NPO混合算法分析天线-载体系统

安装在电大尺寸平台上的天线,载体的影响不容忽视。采用同样基于电流展开的矩量物理光学混合算法,并通过NURBS物理光学法进一步降低复杂结构的建模和计算,将载体对天线的影响用物理光学电流合并到包括天线的在内较小的矩量法区,使矩量法解决天线-载体系统成为可能。通过矩量法和混合算法分析载体对天线性能的影响证明,载体对天线的影响是显著的,混合算法能够在保证精度的前提下提高运算速度,为解决电大尺寸载体上天线的特性提供了良好的途径。     

并行FDTD方法在海面及其上方漂浮目标复合电磁散射中的应用

利用基于图形处理器(Graphics Processing Unit, GPU)的并行时域有限差分(Finite Difference Time Domain, FDTD)法计算一维粗糙海面及其上方二维漂浮目标的复合电磁散射.采用各向异性完全匹配层(Uniaxial Perfectly Matched Layer, UPML)吸收边界作为截断边界, 为了便于并行程序的设计, 在整个计算区域使用UPML吸收边界差分公式进行迭代.利用异步通信技术来隐藏主机和设备之间的通信时间, 同时使用片上的共享存储器提高读取速度, 进一步对程序进行优化, 得到很好的加速比, 证明了该方法的计算高效性.通过与串行FDTD法以及串行矩量法获得的数值结果进行比较, 验证了该并行方法的正确性, 进而研究了海面上方类似舰船漂浮目标的电磁散射特性, 讨论了入射角、海面风速以及目标吃水深度对双站散射系数的影响.