基于混合ACA的缺陷钢轨高效电磁建模

提出了一种基于矩量法(MoM)结合多层快速多极子(MLFMA)和自适应交叉近似(ACA)算法计算目标电磁特性的算法,该算法实现了对电大尺寸复合目标散射计算的加速和内存的降低。对于目标自作用的近场区域,多层快速多极子加速矩量法中的矩阵矢量乘运算,降低了计算的存储和复杂度;对于远场区域,根据阻抗矩阵的低秩特性,采用ACA对其压缩,加速矩阵的填充。矩阵填充按照树形结构划分的单元块间的相互作用依次进行存储,对每一块与块之间的求解采用ACA算法,对矩阵做压缩处理。提出的基于ACA的混合算法能够对2个目标耦合作用的阻抗矩阵进行压缩,缩短矩阵的填充时间并降低内存需求,同时也能够减少迭代求解过程中矩阵向量的计算时间,从而极大缩短电磁散射计算的总时间。数值仿真实验表明该算法比传统方法计算更高效,且计算精确度保持一致。     

求解多尺度目标电磁散射的积分方程快速算法

多层快速卡特森展开算法(Multilevel Accelerated Cartesian Expansion Algorithm,MLACEA)可用于加速电小尺寸结构积分方程矩量法,且矩阵与矢量乘积运算计算复杂度为O(N)量级;MLACEA和多层快速多级子算法(Multilevel Fast MultipoleAlgorithm,MLFMA)均基于八叉树分组结构,便于实现它们的混合快速算法MLA-CEA-MLFMA.该混合算法可大幅度降低模拟合精细结构的电大尺寸目标宽带电磁散射问题的计算复杂度.还详细阐述了求解电场积分方程的MLACEA算法及其与MLFMA算法的混合快速算法MLACEA-MLFMA算法;并通过计算实例对比分析了MLFMA算法与MLACEA-MLFMA混合算法的计算效率.     

用于分析电磁散射问题的快速多极算法

介绍了用于分析电磁散射问题的快速多极算法(FMA)和多层快速多极算法(MLFMA)的基本思想与基本步骤。通过计算实例表明,快速多极算法在计算速度和存贮要求方面比矩量法有明显优势,适合于在现有计算机条件下求解电大尺寸目标的散射问题。     

用于分析电磁散射问题的快速多极算法

介绍了用于分析电磁散射问题的快速多极算法（FMA）和多层快速多极算法（MLFMA）的基本思想与基本步骤。通过计算实例表明，快速多极算法在计算速度和存贮要求方面比矩量法有明显优势，适合于在现有计算机条件下求解电大尺寸目标的散射问题。     

介质涂敷电大尺寸导体柱电磁散射特性的有限元-快速多极混合算法分析

采用有限元-快速多极混合算法分析了介质涂层电大尺寸导体柱的电磁散射特性。与有限元-矩量法相比,快速多极算法将计算复杂度从Ｏ(N2)降低到O(N1.5),大大加快计算速度,减少存储量。计算表明该混合算法对电大复杂涂敷目标电磁特性的分析是灵活而有效的。     

大型阵列结构电磁散射的P-FFT算法

提出利用预校正的快速傅立叶变换(P-FFT)和矩量法(MoM)快速分析电大阵列结构的电磁散射特性.研究了适合于电大尺寸结构近区和远区场计算的格林函数的快速算法,同时,利用Rao-Wilton-Glisson(RWG)函数作为基函数和测试函数,可以考虑阵列单元任意方向的表面电流或磁流分布,并利用P-FFT加速矩量法的矩阵求解,减少内存需求和计算时间.计算结果表明该方法特别适合于大型阵列电磁散射特性的分析.     

三维导体介质复合结构电磁辐射与散射的MLFMA分析

利用多层快速多极子方法(MLFMA)分析三维导体介质复合结构的电磁辐射与散射特性.根据等效原理,介质表面构造Poggio-Miller-Chang-Harrington-Wu(PMCHW)方程,导体表面建立电场积分方程(EFIE).分析了含介质目标MLFMA算法中远区组矩阵矢量相乘运算以及有耗媒质空间中格林函数的平面波展开.利用该方法研究了涂敷目标电磁散射特性以及天线罩对直线阵天线辐射特性的影响.MLFMA的应用降低了计算量和存储量,实现了对电大尺寸目标快速、准确的求解.     

多尺度问题电磁特性叠层矩量法分析北大核心CSCD

论文提出了一种叠层矩量法分析多尺度目标电磁特性。论文采用矩量法直接计算强相互作用区域,多层矩阵压缩方法(MLMCM)和多层快速多极子方法(MLFMA)分别用于加速计算低频和高频作用区域。论文通过使用多分辨ILU(MR-ILU)预条件加速迭代求解矩量法离散多尺度目标产生的病态矩阵方程。通过分析实际多尺度目标电磁特性证明论文方法的有效性。     

基于自适应积分法的三维目标电磁散射的研究

随着物体电尺寸不断变大,传统矩量法计算物体电磁散射和辐射会使计算量和存储量迅速的增加,最终导致无法计算出结果,而自适应积分法解决了矩量法计算量和存储量的问题,使得存储量变小,并利用快速傅里叶变换(FFT)加速了矩阵向量乘积,更加适用于求解电大尺寸的目标。     

电大尺寸物体电磁场问题的混合算法

将MoM(矩量法)-PO(物理光学法)混合算法在电大尺寸物体的电磁计算方面的应用，与传统的有限元法和矩量法等算法相比较，验证其正确性，并体现其计算量小、速度快的优点。使得过去用传统方法无法完成或计算量过大的电大尺寸物体的电磁散射问题真正得以解决。     

含复杂细节结构的金属目标电磁散射ACE-MLFMA 分析

多层快速多极子算法(MLFMA)在计算含复杂细节结构目标的散射问题时,求解效率会迅速下降。本文介绍了快 速笛卡尔展开(ACE)算法及其与MLFMA 的结合,使得原先MLFMA 的最细层能够再局部细分,加速了阻抗矩阵的填充 和迭代求解。本文将该混合算法应用于求解含复杂细节结构目标的电磁散射问题,包括具有尖端的杏仁核和由复杂带线 结构构成的频率选择表面,计算实例验证了该方法求解效率的提高和内存开销的减少,以及算法的可靠性和高效性。     

基于双层ACA算法快速求解单站RCS问题

利用积分方程法计算三维目标单站RCS时,需要逐个角度地进行矩阵方程的求解。为了提高计算效率,本文采用自适应交叉近似算法(ACA)对多角度照射时生成的激励矩阵进行低秩压缩,减少了矩阵方程的求解次数;进一步基于单站角度上的分组方式提出了双层ACA算法,该算法对内存占用极小,提高了算法的并行性,而且更有效地实现了激励矩阵的降秩;最后结合多层快速多极子算法(MLFMA)实现电大尺寸目标的快速求解。数值计算结果表明,该算法能大幅减少大宽角条件下的单站RCS计算时间,具有较高的计算精度和计算效率。     

Solution of combined-field integral equation using multilevel fastmultipole algorithm for scattering by homogeneous bodies

We present an accurate method of moments (MoM) solution of the combined field integral equation (CFIE) using the multilevel fast multipole algorithm (MLFMA) for scattering by large, three-dimensional (3-D), arbitrarily shaped, homogeneous objects. We first investigate several different MoM formulations of the CFIE and propose a new formulation, which is both accurate and free of interior resonances. We then employ the MLFMA to significantly reduce the memory requirement and computational complexity of the MoM solution. Numerical results are presented to demonstrate the accuracy and capability of the proposed method. The method can be extended in a straightforward manner to scatterers composed of different homogeneous dielectric and conducting objects     

并行多层快速多极子的高效预条件技术

多层快速多极子法是基于矩量法的快速算法,具有较低的计算复杂度和存储复杂度,被广泛应用于目标电磁散射特性分析。对于复杂结构电磁目标,由于矩阵条件数较差,往往存在迭代收敛慢甚至不收敛的问题。针对这一情况,文中利用快速多极子的近区矩阵,结合稀疏矩阵方程求解构造了一种高效预条件。数值实例表明该方法相比于块对角预条件效果更好,能有效加速多层快速多极子迭代过程。     

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme     

Electromagnetic Scattering by Arbitrarily Shaped PEC Targets Coated with Anisotropic Media Using Equivalent Dipole-Moment Method

The equivalent dipole-moment method (EDM) is extended and applied in the analysis of electromagnetic (EM) scattering by arbitrarily shaped perfect electric conductor (PEC) targets coated with electric anisotropic media in this paper. The scattering targets are discretized into tetrahedral volume elements in the material region and into triangle patches on the conducting surface, where the volume-surface integral equation (VSIE) is set up. Then the method of moments (MoM) is employed to solve the VSIE. In the impedance matrix, the near field interaction elements are computed by the conventional MoM while the far field interaction elements are modeled by the EDM. The proposed approach is sufficiently versatile in handling arbitrarily shaped objects coated with general electric anisotropic media and is easily constructed through a simple procedure. Numerical results are given to demonstrate the accuracy and efficiency of this method.     

AIM Analysis of Electromagnetic Scattering by Arbitrarily Shaped Magnetodielectric Object

A fast solution to the electromagnetic scattering by large-scale three-dimensional magnetodielectric objects with arbitrary permittivity and permeability is presented. The scattering problem is characterized by using coupled field volume integral equation (CF-VIE). By considering the total electric and magnetic fields, i.e., the sum of incident fields and the radiated fields by equivalent electric and magnetic volume currents, the CF-VIE can be established in the volume of the scatterers. The resultant CF-VIE is discretized and solved by using the method of moments (MoM). For large-scale scattering problems, the adaptive integral method (AIM) is then applied in the MoM in order to reduce the memory requirement and accelerate the matrix-vector multiplication in the iterative solver. The conventional AIM has been modified to cope with the two sets of equivalent volume currents.     

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     

基于超级计算机的矩量法性能分析与优化

复杂目标的精确电磁特性分析往往需要巨大的存储和极长的计算时间。针对这一问题,结合国内发展迅速的超级计算机系统,研究了具有精确高效仿真能力的高性能电磁算法——高阶矩量法。提出了单元预选法来消除矩阵并行填充过程中的无效计算,加速矩阵填充过程。提出了一种具有更少的通信次数和通信量的新型并行LU分解算法,加速矩阵方程求解过程。数值测试表明提出的矩阵并行填充算法和矩阵方程并行求解算法在超级计算机平台上都能获得较高的并行性能,大幅提高了矩量法的仿真能力。