Comparison of fast integral mesh truncation schemes for hybridFE-BI systems

By virtue of their low operation count, the application of fast integral methods such as the fast multipole (FMM) and adaptive integral methods (AIM) result in a substantial quickening of the boundary integral portion of the hybrid finite element-boundary integral (FE-BI) method, independent of the shape of the BI contour. Recently, various versions of the FMM have been proposed, each introducing a different approximation to the implementation of the boundary integral. The main goal of this Letter is to provide a comparison of the effect of these fast integral algorithms on the boundary integral when used in conjunction with the traditional FE-BI method     

合元极技术再认识--一种电大复杂目标散射混合计算技术的考察

合元极技术,即混合有限元、边界元、快速多极子技术,是计算电磁学中近年来日益受到关注的一种精确、高效、通用的技术.本文首先将此技术推广应用于既带涂层又带腔的复杂电大目标电磁散射的计算;接着对合元极技术各种算法的计算精度、迭代收敛速度进行了理论和数值实验的分析研究;然后,从通用性和高效性的角度,对作者采用的不对称合元极技术和近来来其他作者提出的对称合元极技术做了分析比较.最后,本文计算了几种复杂目标的散射截面以证实此项技术的高效、通用.     

有理函数逼近技术在合元极技术中的应用

本文将有理函数逼近技术(Rational Function Approximation Technique,RFAT)应用到合元极技术中以快速求解三维复杂目标的宽频带和宽角度散射特性.有理函数逼近技术是计算数学中的一种重要的函数逼近方法.近年来颇受关注的渐进波形估计技术(Asymptotic Waveform Evaluation,AWE)和基于模型的参数估计技术(Model-Based Parameter Estimation,MBPE)均属于有理函数逼近的范畴.本文将AWE和MBPE两种有理函数逼近技术应用到合元极技术中,并从理论分析和数值性能的角度研究和比较了两种方法的优劣.典型数值实验表明,有理函数逼近技术结合合元极技术能够极大的加速三维复杂目标宽频带和宽角度散射特性的求解.     

一种多层不完全LU分解预处理方法 在合元极技术中的应用

本文将一种多层不完全LU分解预处理方法应用于合元极技术(即混合有限元、边界元、快速多极子技术).理论和数值实验表明,此种预处理方法能大大减少合元极技术的内存需求,同时兼有极高的计算效率.本文首先给出此种预处理方法的构造方式和实施步骤,接着对此种预处理方法在合元极技术中的数值性能进行了理论和数值实验的分析研究;最后,本文计算了几种电大尺寸复杂目标的散射,以展示应用了此种预处理方法的合元极技术的计算能力.     

A Flexible and Efficient Higher Order FE-BI-MLFMA for Scattering by a Large Body With Deep Cavities

The hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is applied to solve the challenge problem of scattering by a large body with deep cavities in this paper. The hierarchical higher order curvilinear vector finite element (HCVFE) is employed to reduce the numerical dispersion error in the FEM and to efficiently model the geometry of the cavity. The coupling approaches are investigated at the interface between the FE region and the BI region for handling the problem of the different order basis functions and meshes used in the FE and BI region. The problems encountered with the previous decomposition algorithm of FE-BI-MLFMA are pointed out and analyzed in this paper. A special algorithm of FE-BI-MLFMA is designed based on the distinct geometry characteristics of deep cavity. Numerical results are presented to demonstrate the accuracy, efficiency and flexibility of the higher order FE-BI-MLFMA for scattering by a large body with big and deep cavities.      

A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals

Diagonalization of the fast multipole method (FMM) for the Helmholtz equation is usually achieved by expanding the multipole representation in propagating plane waves. The resulting k-space integral over the Ewald sphere is numerically evaluated. Storing the k-space quadrature samples of the method of moments (MoM) basis functions constitutes a large portion of the overall memory requirements of the resulting algorithm for solving the integral equations of scattering and radiation problems. In this paper, it is proposed to expand the k-space representation of the basis functions by spherical harmonics in order to reduce the sampling redundancy introduced by numerical quadrature rules. Aggregations, plane wave translations, and disaggregations in the realized multilevel fast multipole method (MLFMM) are carried out using the k-space samples of a numerical quadrature rule. However, the incoming plane waves on the finest MLFMM level are expanded in spherical harmonics again. Thus, due to the orthonormality of spherical harmonics, the testing integrals for the individual testing functions are simplified into series over products of spherical harmonics expansion coefficients. Overall, the resulting MLFMM can save a considerable amount of memory without compromising accuracy and numerical speed.     

On the formulation of hybrid finite-element and boundary-integralmethods for 3-D scattering

This paper studies, in detail, a variety of formulations for the hybrid finite-element and boundary-integral (FE-BI) method for three-dimensional (3-D) electromagnetic scattering by inhomogeneous objects. It is shown that the efficiency and accuracy of the FE-BI method depends highly on the formulation and discretization of the boundary-integral equation (BIE) used. A simple analysis of the matrix condition number identifies the efficiency of the different FE-BI formulations and an analysis of weighting functions shows that the traditional FE-BI formulations cannot produce accurate solutions. A new formulation is then proposed and numerical results show that the resulting solution has a good efficiency and accuracy and is completely immune to the problem of interior resonance. Finally, the multilevel fast multipole algorithm (MLFMA) is employed to significantly reduce the memory requirement and computational complexity of the proposed FE-BI method     

Implementation and experiments of a hybrid algorithm of theMLFMA-enhanced FE-BI method for open-region inhomogeneouselectromagnetic problems

Although the computational complexity of the finite-element boundary-integral (FE-BI) method is significantly reduced by the multilevel fast multipole algorithm (MLFMA), this MLFMA-enhanced FE-BI solution experiences a very slow convergence for some complex inhomogeneous problems. A hybrid algorithm, combining direct methods with iterative methods, is designed. to speed up the rate of convergence of this MLFMA-enhanced FE-BI solution. This hybrid algorithm is efficiently implemented with the aid of a newly developed package, SuperLU, of the LU decomposition solver. Numerical experiments are performed for scattering by a coated Northrop wing to demonstrate the efficiency of this hybrid algorithm. More importantly, the thorough investigation of the numerical experiments clearly shows the better accuracy, stability, and robustness of this hybrid algorithm over the conventional algorithms     

A Hybrid SIM-SEM Method for 3-D Electromagnetic Scattering Problems

A new method combining the spectral integral method and spectral element method (SIM-SEM) is proposed to simulate 3-D electromagnetic scattering from inhomogeneous objects. In this hybrid technique (a special case of the finite element boundary integral (FEM-BI) combination), the SEM with the mixed-order curl conforming vector Gauss-Lobatto-Legendre (GLL) basis functions are used to represent the interior electric field with high accuracy, while the SIM on a cuboid surface is used as an exact radiation boundary condition. The Toeplitz property of the SIM matrix is utilized to reduce the memory and CPU time costs in an iterative solver by using the fast Fourier transform algorithm. Unlike the traditional FEM-BI combination where the BI portion usually dominates the computational complexity, the computational costs are much lower in the SIM-SEM method. Numerical results verify the accuracy and capability of this method, confirming that the SIM-SEM method is a good alternative for solving scattering problems from inhomogeneous objects.      

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.     

Acceleration of on-surface MEI method by new metrons and FMM for 2-D conducting scattering

A new kind of metron is proposed and rapid integration provided by fast multipole methods (FMM) is implemented to dramatically reduce the CPU time of finding the MEI coefficients in the on-surface measured equation of invariance (OSMEI) method. The numerical example of the scattering of a large conducting elliptical cylinder shows that the computation speed is at least one order of magnitude faster than that of the original OSMEI, where sinusoidal metrons are used, and about 25% faster than that of the FMM, where the iteration method is used.     

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。     

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。     

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。     

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     

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。     

多层快速多极子方法中转移因子的修正拉格朗日内插技术

利用多层快速多极子方法,许多电大尺寸问题现已能在有限的计算机条件下得以解决.在多层快速多极子方法中,转移计算是主要的计算工作量,所涉及的转移因子的计算和存储方法也直接影响方法效率.为实现转移因子的快速计算和低存储,本文提出一种高效的修正拉格朗日内插技术.通过引入场源间距的修正因子,不同场源间距的转移因子可由局域内插快速计算.与传统多层快速多极子方法中计算转移因子的方法相比,该方法显著降低了转移因子的存储量和计算量,并具有可靠的计算精度.     

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。     

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     

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