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.     

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.     

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。     

并行处理技术在电大尺寸复杂目标电磁散射中的应用

虽然快速多极子算法FMM(Fast Multipole Method)和多层快速多极子算法MLFMA(Multi-Level Fast Multipole Algorithm)是解决复杂目标电磁散射问题比较有效的方法,但是当问题的规模较大时,传统的串行FMM 和MLFMA难以胜任.本文在工作站网络系统NOW(Network Of Workstation)上采用并行处理技术来解决电大尺寸复杂目标电磁散射问题.结果表明:本文提出的并行解决方案与国内外相关成果相比不仅更具实用性,并行效率达到54%以上,且解决了串行方法难以解决的电磁散射问题,本文在四台DEC工作站构成的NOW系统上用32小时完成了未知量为160,000的雷达散射截面的计算.     

适用于电磁混合源散射求解的新型积分方程数值方法

含腔导电目标电磁散射的混合场积分方程求解方法中,将出现电场积分方程算子和磁场积分方程算子同时作用于待求混合源的复杂情况,使计算复杂度大为提高.本文导出"均衡混合场积分方程"及其数值方法,使作用于电流和磁流的积分算子完全相同,大大简化了计算.均衡混合场积分方程与多层快速多极子方法(MLFMA)结合使用,可以方便地求解含腔导体目标的电磁散射.本文给出的数值实例充分证明了这一方法的高精度和高效率.     

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。     

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。     

基于并行MLFMA的SAR舰船目标RCS计算

为提高合成孔径雷达（SAR）图像仿真效果,针对SAR图像中舰船目标雷达散射截面（RCS）计算的精度和效率问题,在利用几何建模方法构建三维舰船模型的基础上,采用并行多层快速多极子算法（MLFMA）计算了舰船目标RCS并分析了该算法的并行加速比。仿真实验表明,并行MLFMA算法适用于高频范围内较大尺寸舰船目标RCS的计算,比物理光学法（PO）和物理光学与矩量混合算法（PO—MOM）具有更高的计算精度且并行方案能明显提高求解目标RCS的效率。     

MLFMA/VIE-MoM大型矩阵方程的快速迭代求解方法

 本文针对体积分方程矩量法(VIE-MoM)分析三维非均匀介质电磁散射问题所导出的大型矩阵方程的求解问题, 基于多层快速极子技术(MLFMA)算法研究了快速近似迭代方法.提出了一种基于MLFMA分组方案对系数矩阵进行重组并提取强耦合元素的近场预条件器的构造方法,有效地提高了广义最小余量法(GMRES)的迭代收敛速度.提出了一种在迭代计算过程中的近似矩阵向量乘积方案,明显降低了单步计算过程中MLFMA远区耦合作用的计算时间.计算实例表明,采用本文的迭代加速技术可使计算速度提高3至5倍,有效地提高了VIE-MoM大型矩阵方程的迭代求解速度.     

混合ACA和MLFMA方法计算复合目标电磁散射

采用矩量法(MoM)计算电大尺寸的复合目标的电磁散射。为了能够高效快速地计算电大尺寸三维复合目标的电磁散射,提出一种新的混合方法,将自适应交叉近似(ACA)算法和多层快速多级子(MLFMA)算法相结合,共同加速矩量法的计算。其中,MLFMA用于加速目标与自身的作用,ACA用于加速目标与其他目标的相互作用。提出的混合算法在计算复合目标电磁散射时,可降低运算存储,缩短阻抗矩阵填充时间,并且能够加快矩阵矢量乘,且不影响计算精确度。数值算例表明,所提快速算法能够在保证电磁散射计算精确度前提下,比传统方法更高效。     

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 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.     

An Efficient Implementation of the Combined Wideband MLFMA/LF-FIPWA

An efficient implementation of the low frequency fast inhomogeneous plane wave algorithm (LF-FIPWA) combined with the multilevel fast multipole algorithm (MLFMA) is presented. The seamless combination of the LF-FIPWA with the MLFMA renders a powerful method applicable for a wide frequency range. As the MLFMA is already well established we will describe possibilities for an efficient formulation of the LF-FIPWA: An implicit filtering reduces the bandwidth of the integrand. An interpolation of the excitation vectors is introduced which avoids dealing with the in general complex angles. An adaptive quadrature rule on the path in the complex plane further increases the efficiency. We present a simple but accurate interpolation and anterpolation method on this path. In addition, for symmetric objects or for perfectly conducting ground the incorporation of a symmetry wall is described.      

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     

电大均匀介质目标三维散射的并行多层快速多极子计算

实现了计算电大均匀介质体散射问题的高效混合并行混合场积分方程(Electric and Magnetic Current Combined-Field Integral Equation, JMCFIE)求解, 在单纯消息传递接口(Message Passing Interface, MPI)并行基础上采用共享存储并行编程(Open Multi-Processing, OpenMP)进一步提升性能.该混合MPI与OpenMP的并行多层快速多极子技术通过灵活的进程和线程策略, 提升了负载平衡和可扩展性.数值实验展示了此混合MPI与OpenMP的并行多层快速多极子技术的计算能力, 计算了不同尺寸的电大目标体(包含一个半径120 m、1.1亿未知数目的介质球).     

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.     

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     

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。     

MLFMA分析复杂载体平台上天线问题

该文分析了导体介质复合结构平台上线天线的辐射问题。利用等效原理建立EFIE-PMCHW表面积分方程组,定义线、面和连接基函数描述复杂结构上电流分布,分析了导体介质分界面处基函数的处理;利用多层快速多极子方法(MLFMA)加速迭代求解过程中的矩阵矢量相乘运算,并用于有耗媒质求解。MLFMA的运用极大地提高了求解实际电大问题的能力。数值计算结果验证了方法的正确性和高效性。