Parallel multilevel fast multipole method for solving large-scale problems

The Multilevel Fast Multipole Method (FMM) is a well-established method and can be applied to solve electromagnetic (EM) scattering problems. Compared with other traditional methods, it requires less computational time and memory. However, constrained by a single processor's speed and memory limitations, the problem size that can be solved by serial implementation is still relatively small. For a million-unknown target, the computational time on a single processor is intolerable, and memory could be easily exhausted. Parallel-computing technology, which can utilize multiprocessors, provides an efficient way to solve electrically large-scale EM problems. This paper will focus on discussing the parallel methodologies applied to a multilevel FMM code, as well as demonstrating the computational efficiency of the parallel approach.     

A fast multipole method for layered media based on the application of perfectly matched layers - the 2-D case

An efficient fast multipole method (FMM) formalism to model scattering from two-dimensional (2-D) microstrip structures is presented. The technique relies on a mixed potential integral equation (MPIE) formulation and a series expression for the Green functions, based on the use of perfectly matched layers (PML). In this way, a new FMM algorithm is developed to evaluate matrix-vector multiplications arising in the iterative solution of the scattering problem. Novel iteration schemes have been implemented and a computational complexity of order O(N) is achieved. The theory is validated by means of several illustrative, numerical examples. This paper aims at elucidating the PML-FMM-MPIE concept and can be seen as a first step toward a PML based multilevel fast multipole algorithm (MLFMA) for 3-D microstrip structures embedded in layered media.     

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.     

有耗半空间环境中导体目标电磁散射的快速分析

应用快速多极子方法求解有耗半空间环境中任意三维金属体的雷达散射特性.对于基函数与测试函数的近场组作用,我们用离散复镜像法严格处理半空间并矢格林函数.在处理远场区时,我们利用实镜像源和反射系数近似计算交界面处远场的作用.通过位于有耗半空间三面角反射器、立方体证明了方法的正确性和有效性.另外,将多分辨预处理器和快速多极子方法结合使得矩阵求解器的迭代次数和计算时间减少数倍.     

Fast multipole method for scattering from an arbitrary PEC targetabove or buried in a lossy half space

The fast multipole method (FMM) was originally developed for perfect electric conductors (PECs) in free space, through exploitation of the spectral properties of the free-space Green's function. In the work reported here, the FMM is modified, for scattering from an arbitrary three-dimensional (3-D) PEC target above or buried in a lossy half space. The “near” terms in the FMM are handled via the original method-of-moments (MoM) analysis, wherein the half-space Green's function is evaluated efficiently and rigorously through application of the method of complex images. The “far” FMM interactions, which employ a clustering of expansion and testing functions, utilize an approximation to the Green's function dyadic via real image sources and far-field reflection dyadics. The half-space FMM algorithm is validated through comparison with results computed via a rigorous MoM analysis. Further, a detailed comparison is performed on the memory and computational requirements of the MoM and FMM algorithms for a target in the vicinity of a half-space interface     

The fast multipole method (FMM) for electromagnetic scatteringproblems

The fast multipole method (FMM) developed by V. Rokhlin (1990) to efficiently solve acoustic scattering problems is modified and adapted to the second-kind-integral-equation formulation of electromagnetic scattering problems in two dimensions. The present implementation treats the exterior Dirichlet problem for two-dimensional, closed, conducting objects of arbitrary geometry. The FMM reduces the operation count for solving the second-kind integral equation from O(n³) for Gaussian elimination to O(n^4/3) per conjugate-gradient iteration, where n is the number of sample points on the boundary of the scatterer. A sample technique for accelerating convergence of the iterative method, termed complexifying k, the wavenumber, is also presented. This has the effect of bounding the condition number of the discrete system; consequently, the operation count of the entire FMM (all iterations) becomes O(n^4/3). Computational results for moderate values of ka, where a is the characteristic size of the scatterer, are given     

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。     

三维大纵横比目标散射的快速精确求解

采用积分方程法严格求解三维大纵横比目标的电磁散射。在积分方程法的迭代求解中用快速我极子法（ＦＭＭ）加速矩阵与矢量的相乘计算,同时运用快速傅里叶变换（ＦＦＴ）进一步提高快速多极子方法中的转换预计算,数值结果表明：这种快速多极子法－快速傅立叶变换方法（ＦＭＭ－ＦＦＴ）特别适合于三维大纵横比目标的散射求解。     

快速分析电大腔体电磁散射的混合算法

为提高电大腔体电磁散射分析的效率,提出将迭代物理光学法（IPO）与快速多极子方法（FMM）相结合的混合算法IPO＋FMM,给出该混合算法的数学模型推导,该算法可将每迭代步的计算量由O（N^2）降到O（N^1.5）,最后分析了二种不同形状的电大尺寸腔体的雷达散射截面。数值结果表明,该混合算法与IPO算法相校,精度相当但效率有显著提高。     

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.     

基于固定实镜像平面波展开的快速多极子方法计算微带结构问题

将快速多极子算法应用于微带结构的一个关键技术是将矩量法中描述远区单元相互作用的Green函数用加法定理进行平面波展开.本文提出用固定实镜像方法拟合微带结构谱域Green函数进行平面波展开,对比目前常用的复镜像闭式平面波展开方法,该方法具有展开收敛性好,物理概念清晰,Green函数宽频插值方便等特点.计算实例表明了该方法的有效性和可靠性.     

快速多极子和遗传算法在电磁成像中的应用

从电磁场的积分方程出发,利用快速多极子（ＦＭＭ）加速矩量法（ＭｏＭ）计算导体柱电磁散射的过程;以散射场的测量值与计算值的平均偏差为目标函数,以导体柱截面形状参数为优化变量,利用遗传算法（ＧＡ）进行优化迭代,来重构目标导体柱的电磁影像。对美国空军ＲＯＭＥ实验室提供的实际数据（Ｉｐｓｗｉｃｈ数据）进行了电磁成像;并给出了对较大导体柱电磁成像的例子。     

Electromagnetic inverse scattering of multiple perfectly conducting cylinders by differential evolution strategy with individuals in groups (GDES)

The differential evolution strategy with individuals in groups (GDES) is proposed to solve the electromagnetic inverse scattering of multiple perfectly conducting cylinders with transverse magnetic wave incidence. The inverse problem is to locate the cylinders and reconstruct their contours, besides the determination on the number of cylinders. The governing electric field integral equations for the scattering problem are expressed as surface integrals over the cylinder contours. The scattering problem is solved using point-matching method with pulse basis and Dirac test functions. The inverse problem is cast into an optimization problem and solved using the GDES. Numerical reconstruction results show that both the quality of the reconstructed profile and the convergence performance are significantly improved, as compared to the original DES.     

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。     

Multilevel fast multipole algorithm for electromagnetic scatteringby large complex objects

The fast multipole method (FMM) and multilevel fast multipole algorithm (MLFMA) are reviewed. The number of modes required, block-diagonal preconditioner, near singularity extraction, and the choice of initial guesses are discussed to apply the MLFMA to calculating electromagnetic scattering by large complex objects. Using these techniques, we can solve the problem of electromagnetic scattering by large complex three-dimensional (3-D) objects such as an aircraft (VFY218) on a small computer     

An alternative solution of the scattering from an anisotropic cylindrical dielectric shell

A method based on the approximate wave functions for anisotropic media and the mode-matching approach is developed to solve the problem of the electromagnetic scattering from an anisotropic cylindrical dielectric shell. The cylindrical shell is assumed to be infinite in length, and it is illuminated by a plane wave or a cylindrical wave from a line source. The problem is two-dimensional and the solutions to both types of polarization (TE and TM) are presented. The validity of this solution is verified by comparing the numerical results with those in literatures and the previous calculations based on the exact wave functions for anisotropic media. Numerical results show the higher computational efficiency of the present method for bounded anisotropic media.     

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。     

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。     

FMM算法用于二维复杂散射体的RCS计算

利用快速多极子算法(FMM)计算任意形状二维电大尺寸导体加介质体目标的电磁散射，介质体为镶嵌在电大尺寸金属体上的有耗介质。建立金属一介质体的混合积分方程，用共轭梯度法和场量叠代的方法计算散射场，在叠代过程中用快速多极子方法，大大降低计算时间和减小内存要求。数据结果表明该方法的准确和高效。     

Indoor field strength prediction based on FMM

1 Introduction With the popularization of personal communication service (PCS), indoor radio propagation has attracted more attention, especially for ultra-wideband (UWB) signals. Ultra-wideband communication systems have very high data rates (at least 10…