多层快速多极子算法中的两步插值技术

多层快速多极子算法(MLFMA)在快速多极子算法(FMM)的基础上按多层聚集、层间转移和多层扩散的思路以达到优化矩阵向量积的运算的目的,其中多层聚集和多层扩散过程,随着层数递增,角谱积分采样点数逐层递增,为了快速计算角谱积分,需要采用插值技术和反插值技术以提高计算效率.应用两步插值技术替代传统的单步插值技术,大幅提高了多层快速多极子层间插值反插值操作的计算效率,对于应用普通个人计算机求解特大电大尺寸问题,具有重要意义.     

快速计算地面上车辆目标的电磁散射特性

为快速计算地面上车辆目标的电磁散射特性,实现适用于半空间环境的多层快速多极子方法.对于近区项,利用严格的半空间并矢格林函数进行计算;对于远区项,首先将半空间格林函数分解为直射项和反射项,然后采用实镜像方法计算反射项.方法物理概念清晰,与目前常用的离散复镜像方法相比,具有良好的收敛性和稳定性,大大降低计算时间和内存需求.实例计算并分析地面上汽车模型的电磁散射特性.     

三维声学多层快速多极子边界元及其应用

快速多极子边界元算法可以加速矩阵和向量乘法运算, 将传统边界元算法的计算量和内存占用量分别降为O(N log²N)和O(N), 适用于大型声学模型模拟计算. 本文发展了一种基于Burton-Miller方程的三维多层声学快速多极子边界元算法. 将新的自适应树状算法应用到对角形式的快速多极子边界元算法, 并使用最新提出的解析式源点矩计算公式, 进一步提高了快速多极子边界元的计算效率. 绝对软球体在内部共振频率处的散射声场计算, 验证了所发展算法在共振频率处求解的正确性. 与Bapat所提供的程序在多脉动球体辐射声场计算精度的比较, 验证了算法及程序在大型模型声学计算中的准确性, 同时显示了其求解的高效性. 最后, 将该算法用于车内声场及水下声学探测的分析计算.     

二维声学多层快速多极子边界元及其应用

与模型自由度的平方成正比的存储量和计算量,使传统边界元无法应用到大型模型的计算。为此,发展了一种二维声学多层快速多极子边界元算法。通过二维Helmholtz核函数展开理论的简要介绍,推导了源点矩计算、源点矩转移、源点矩至本地展开转移、本地展开转移公式,并详细描述了二维声学快速多极子边界元算法的具体实现步骤。使用快速傅里叶插值进行源点矩和本地展开系数的多层传递。采用对角左预处理方法,改善边界方程的条件数,减少迭代求解次数。最后通过数值算例,验证了所发展的二维声学快速多极子算法的正确性和高效性。      

MLFMA用于三维电大复杂腔体电磁散射特性的快速计算

基于迭代物理光学法的多层快速多极子算法可高效、快速求解电大腔体的散射特性,给出混合算法的迭代公式.对工程上常见的弯曲较缓慢的S弯腔体,通过合适的分段结构化分组,避免两组之间存在的部分面元遮挡的情况,应用广义互易积分处理带有复杂终端的腔体.数值计算结果表明,所用方法准确并能极大地提高计算速度.     

积分方程平面反射阵电磁建模技术北大核心CSCD

针对基于空间功率合成的空馈平面反射阵(FLAPS)型高功率微波辐射器的高效率电磁仿真需求,应用积分方程方法结合多尺度混合电磁建模技术MLFMA-MLACE进行问题的电磁建模及求解,主要过程包括:针对设计模型进行多尺度几何建模;在宏观层面采用多层快速多极子加速矩矢相乘;在微观层面采用多层笛卡尔展开加速求解。结合W波段的FLAPS初步模型,利用传统多层快速多极子技术(MLFMA)进行了精度验证,对于混合方法在仿真中的适用性、模型等效处理程度的影响以及计算成本等进行了分析。结果表明,该方法在内存及计算时间方面显著地提高了效率,论文还对后续改进方向进行了讨论。     

撤稿声明

本刊于2011年3月发表向道朴等人的研究论文多层快速多极子算法中的两步插值技术(《计算物理》28卷第2期237—242页)后,发现该文与另一篇文章(Ergül ,van den Bosch,and Gürel L.Two-step     

消声器声学性能预测的子结构快速多极子边界元法

鉴于快速多极子边界元法的应用主要局限于单区域声学问题计算,发展基于子结构技术的快速多极子边界元法以计算多区域声场问题,介绍基本原理、具体实施过程以及优缺点.以带有插进口管的膨胀腔消声器为例,应用子结构快速多极子边界元法和传统边界元法计算其传递损失,通过与实验测量结果的比较,验证方法的有效性和计算精度.研究表明,快速多极子边界元法与传统边界元法相比,节点数越多,其在节省计算时间,减少计算量等方面的优势越明显.     

半空间背景下目标电磁散射等效模型研究

在电磁场积分方程方法框架下,应用等效原理求解了半空间背景下目标的电磁散射问题,可针对目标仅处于半空间界面单侧及目标跨越半空间界面处于半空间两侧的几何相对位置。与传统的半空间格林函数计算方法不同的是,这一方法使用的是各自介质的自由空间格林函数,因此可以回避索墨菲积分并且可以很方便与快速算法(如多层快速多级子)相结合,并对求解临近半空间界面的目标获得较好的收敛性。在等效原理方法中需要用有限的界面等效无限大半空间界面,因此采用了锥形入射波以降低开放边界引起的边缘效应。不同于一般目标的远场雷达散射截面表达,在该模型下,半空间电磁散射的远场描述需要用差场雷达散射截面。给出的算例能与现有文献以及仿真软件很好的吻合,并可作为实用工具分析半空间背景对目标远场响应的影响。     

电子稳像的分层位平面全局运动估计算法

提出一种分层位平面匹配的快速全局运动估计算法.算法充分利用多分辨率思想,在每一层选用不同位平面进行匹配以找到运动矢量;利用层内块运动的空间相关性和层间矢量传递性,来自适应地选择搜索起始点;同时设定阈值,对运动矢量满足准确度的子块,直接结束搜索;将所得到的各子块的运动矢量作为集合,根据其统计规律,找到出现概率最大的样本作为正确的全局运动矢量.实验表明,该算法计算速度快,且与块匹配全搜索相比,其误差小于半个像素,能够达到快速准确进行全局运动估计的能力.     

基于新型混合场积分方程的半空间三维均匀介质目标电磁散射分析

利用介质半空间格林函数,将一种混合场积分方程(JMCFIE)推广应用到有耗半空间的均匀介质的散射分析中,以减少离散矩阵方程迭代求解时所需的迭代步数,提高矩量法(MoM)对半空间介质目标散射分析的求解效率.数值算例验证了方法的准确性和有效性.     

Electromagnetic volume scattering in the half-space: a moment-method analysis without Sommerfeld integrals or their approximations

Traditionally, in moment-method analyses of electromagnetic scattering, the elements of the impedance matrix are calculated as convolutions of the basis elements with the appropriate dyadic Green's function. However, for scattering in the half-space, the vertical and azimuthal copolar terms of the Green's function require evaluation of Sommerfeld integrals which are computationally burdensome. In this paper, it is shown that, in populating the impedance matrix for the half-space problem, evaluation of Sommerfeld integrals is, in fact, not necessary. For monochromatic excitation, the plane-wave expansion of the scattered field constitutes a Fourier transform, in the horizontal plane, of a vector spectral function. This vector function results from the convolution, in the vertical dimension, of the respective angular spectra of the Green's function and the equivalent current. On application of the moment method, through the Weyl identity, the impedance-matrix elements corresponding to the singular terms of the Green's function are convolutions in the horizontal plane of spherical potentials, and Fourier transforms of scalar spectral functions. These scalar functions are derived from the basis elements and, with a judicious choice of basis, they are well behaved and of compact support, and consequently their Fourier transforms can be computed as FFTs.     

The complex equivalent source method for sound propagation over an impedance plane

The sound field caused by a monopole source above an impedance plane can be calculated by using a superposition of equivalent point sources located along a line in the mirror space below the plane. Originally, such an approach for representing the half-space Green's function was described by Sommerfeld at the beginning of the last century, in order to treat half-space problems of heat conduction. However, the representation converges only for masslike impedances and cannot be used for the more important case of reflecting planes with springlike surface impedances. The singular part of the line integral can be transformed into a Hankel function, which shows that surface waves are contained in the whole solution. Unfortunately, this representation suffers from the lack of validity at certain receiver points and from restrictions on wave number and impedance range to ensure the necessary convergence. The main idea of the present method is to use also a superposition of equivalent point sources, but to allow that these sources can be located at complex source points. The corresponding form of the half-space Green's function is suitable for both masslike and springlike surface impedances, and can be used as a cornerstone for a boundary element method.     

半空间电大涂敷目标散射的高频分析方法

研究了半空间内(海面,地面)电大尺寸涂敷目标散射的高频求解方法.将半空间并矢格林函数引入物理光学方法中,对半空间复杂环境影响进行考虑,并利用阻抗边界条件考虑涂敷目标表面的复杂电磁散射,推导出半空间物理光学分析方法,同时结合图形电磁学,对半空间电大涂敷目标进行消隐判断,提取像素面元法矢量和深度缓存等有效信息,快速有效地计算了半空间电大涂敷目标的雷达散射截面.数值结果证明了方法的有效性和准确性. 关键词： 半空间物理光学方法 半空间并矢格林函数 图形电磁学 雷达散射截面     

基于半空间FDTD的近远场外推方法: TE情形

研究基于半空间时域有限差分(FDTD)计算中TE情形的远区散射场计算方法.先将半空间Green函数代入势函数,推导远区纵向磁场的计算公式,对各空间内电磁流和对应的相位进行详细分析.再计算两个半空间模型的远区散射场,结果表明:该方法是正确和有效的.针对日本96式装甲车的计算发现,单站雷达探测系统位于战车正上方时具有最好的探测效果.     

Green's functions for a volume source in an elastic half-space

Green's functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green's function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green's function obtained following the first approach. The Green's function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.     

Radiation of ultrasound into an anisotropic solid

A half-space, x₃ 0, of a transversely isotropic solid whose axis of symmetry makes an angle with the x₃-axis, is subjected to a spatially uniform time-harmonic distribution of normal surface tractions over a circular area of the plane x₃ = 0. The wave motion radiated into the half-space is investigated. Using an integral representation for the displacement components the problem is first reduced to a system of singular integral equations for the displacements on the surface x₃ = 0. This system is solved by the boundary element method over a truncated area, where use is made of recently derived simplified forms of the Green's functions. The results show the skewing of the beam as the angle between the axis of symmetry of the transversely isotropic solid and the normal to the surface of the solid is increased.     

A conjugated infinite element method for half-space acoustic problems

Many acoustic problems (especially in environmental acoustics) involve half-space domains bounded by a plane subjected to normal admittance boundary conditions. In the "low" frequency domain, the numerical treatment of such problems usually relies on boundary element methods based on a particular Green's function suited for the half-(admittance) plane. In the present paper, an alternative hybrid finite/infinite element scheme is proposed. The method relies on a direct treatment of nonhomogeneous boundary conditions along infinite element edges (or faces). The procedure is validated through comparisons with an available reference solution.     

Origin of Bragg-Coulomb high-Tc superconductivity Green''s function and diagram method for umklapp e-e scattering

The Green's function method and diagram technique for umklapp electron-electron scattering mediated by the screened Coulomb interaction in layered anisotropic conductors are examined. Gor'kov-type equations and their general solution for anomalous and normal temperature Green's functions are derived taking into account umklapp scattering of all orders. Explicit equations for dielectric and superconducting order parameters, including coexistent Bragg and BCS pairing, are found. The possibility of the first-order phase transition to the superconducting state is discussed. The theory elucidates the origin of Bragg-Coulomb high-T_c superconductivity, proposed by the authors.