一种求解电磁散射问题的快速迭代法

结合快速多极子技术,提出了一种新的迭代方法--快速多极子-加窗测试迭代法来求解任意截面电大尺寸导体柱的电磁散射问题.该方法结合了电磁场积分方程数值求解技术和高频近似概念,将散射体阴影区的误差场量用实窗函数压缩,并在散射体表面构造单点测试方程,建立了迭代求解式.迭代过程中的矩阵向量乘积通过快速多极子法加速.数值实验表明该方法解电磁散射问题快速、有效,仅需几次迭代即可收敛至足够精度,迭代次数不随问题规模增加,其计算量仅略高于线性复杂度.     

求解多层介质中声波传播问题的一种边界元方法

针对多层介质中声波的传播问题,将其中偶数(或奇数)层内的声波用一种单双层混合位势的形式来表示,再应用Green定理表示出其余层的声波并形成相应的边界积分方程.如果区域有M层时,传统的边界元方法最终将形成2M个边界积分方程并对应2M个未知函数,而应用上述方法求解该问题时,最终只形成M个边界积分方程以及对应M个未知函数,从而使得求解的方程和未知数的个数都减少了一倍.最后,通过对数值算例的求解,验证了该方法的可行性及精确性.     

求解周期结构中声波传播问题的一种边界元法

本文应用边界积分方程方法(边界元法)求解无限长周期结构中声波的传播问题,根据散射体的周期排布方式,将无限个散射体对应无限个边界积分方程的求解问题转化为在某一个单位块中有限个边界积分方程的求解,从而使得该问题的数值求解变得简单可行.然后将该方法应用于声子晶体能量禁带的预测中,通过对数值算例的求解以及与其他方法求解结果的比较,验证了本文所提出方法的可行性和准确性.     

并行计算水下大尺度弹性壳体的低频声散射

有限元与边界元耦合模型是研究水下弹性壳体目标低频声散射常用的数值方法。应用该模型计算大尺度弹性目标的声散射时需要大量的计算时间与存储空间,采用并行数值的方式可以解决这一问题。首先并行计算生成有限元矩阵和边界元矩阵,然后应用并行化的广义极小残差(GMRES)迭代算法求解大型非对称线性方程组。详细叙述了并行GMRES(m)迭代算法的执行过程,并以球壳的声散射计算为例分析了迭代步数对算法收敛情况的影响。最后计算了Benchmark目标模型的低频散射声场,分析了其收发分置散射目标强度以及表面声场的分布。     

电场积分方程的快速求解

矩量法(MOM)离散电场积分方程(EFIE)得到稠密的线性方程组,它可以用迭代法(比如本文中的TFQMR方法)求解.每次迭代过程中,矩阵与向量的乘积的复杂度为O(N2).采用多层快速多极子方法(MLFMM),可将其降到O(N log N).采用基于球谐变换的快速傅立叶变换,可进一步加快MLFMM的层间插值计算.数值结果显示MLFMM求解EFIE是可行的.     

高振荡非齐次动力系统的有效数值算法

为实现高振荡问题模型方程的有效数值求解,基于高振荡积分的渐进积分算法,针对随时间高频率振荡的非齐次线性动力系统给出有效的数值算法.基于变分常数公式将非齐次动力系统重新表示为指数形式,利用Magnus积分方法求解指数部分,利用渐进积分算法求解高振荡的积分项.数值实验表明：该算法求解精度随振荡频率的增大而提高,且简单易用,也可以容易推广到多个方程的情形.     

基于时域积分方法分析PCB串扰问题

采用时域积分方程法及改进型节点分析法对PCB板间导线的串扰问题进行建模.时域积分方程法以等效原理为基础,在矩量法应用中加入时间因子的考虑,并采用RWG基函数将模型划分为多个三角面元,从而将导线间的影响以散射的角度来表达.另外采用改进节点分析法对电路边界不连续性进行求解,从而懈决了有限电导率导体和各向同性介质相结合情况下的串扰问题.最后在多层PCB传输线的算例中,计算给出了不同条件下输出电压和串扰电压波形的时域变化,从而对PCB板间信号完整性做出了分析.     

粗糙面上2D目标散射的KA-CG方法

针对TE极化下粗糙面上方的目标散射问题,提出了粗糙面的基尔霍夫近似(KirchhoffApproximation,KA)计算与目标的共轭梯度法(Conjugate Gradient,CG)求解相结合的混合算法,无需数值求解粗糙面的EFIE,节省了大量的计算时间。提出目标与粗糙面的快速互耦迭代算法:每一次迭代中,首先用上次求得的目标表面场计算粗糙面的差值感应场,代入目标积分方程求解右端激励项,再用CG方法求解目标的EFIE获得新的目标表面场。多次迭代直至目标的表面感应场收敛。结合Monte-Carlo方法迭代计算了二维Gauss粗糙面上柱状目标的散射,数值分析其散射峰值的角度性分布。     

多层快速多极子算法并行实现的数据划分策略

虽然多层快速多极子算法在解决大尺度电磁散射问题中表现出了很好的效率,但是,当未知量达到千万时,由于复杂的结构和计算该算法很难再保持高效的计算能力。为了解决负载均衡引起的性能瓶颈问题,提出多层快速多极子算法基于八叉树的多层结构并行数据划分策略。该方法包括根据树结构中分布层和共享层不同特征的单独处理,也包括解决数据冲突的转移层的处理方法和为了减少分布存储系统中的通信时间而在分布层引入的冗余技术。实验结果表明多层快速多极子算法并行计算的开销明显减少,并且能够获得比较高的并行效率。     

含陀螺效应的声表面波波动方程的求解

含陀螺效应的声表面波(SAW)波动方程的求解是分析旋转压电基体SAW传播特性和设计SAW角速度传感器的理论基础.以旋转条件下压电基体声表面波方程的建立和求解为研究内容,推导了含陀螺效应的Christoffel方程的一般表达式,提出了在求解中必须注意对解耦波的判别及进行相应的处理,设计了计算机数值求解的软件,并给出了流程.以新型压电材料硅酸镓镧作为求解的实例,验证了算法的可行性.理论与算法可为与陀螺效应有关的SAW器件的设计提供参考.     

A new fast multipole boundary element method for two dimensional acoustic problems

A new fast multipole boundary element method (BEM) is presented in this paper for solving large-scale two dimensional (2D) acoustic problems based on the improved Burton–Miller formulation. This algorithm has several important improvements. The fast multipole BEM employs the improved Burton–Miller formulation, and successfully overcomes the non-uniqueness difficulty associated with the conventional BEM for exterior acoustic problems. The improved Burton–Miller formulation contains only weakly singular integrals, and avoids the numerical difficulties associated to the evaluation of the hypersingular integral, it leads to the numerical implementations more efficient and straightforward. Furthermore, the fast multipole method (FMM) and the approximate inverse preconditioned generalized minimum residual method (GMRES) iterative solver are adopted to greatly improve the overall computational efficiency. The numerical examples with Neumann boundary conditions are presented that clearly demonstrate the accuracy and efficiency of the developed fast multipole BEM for solving large-scale 2D acoustic problems in a wide range of frequencies.     

Fast multipole method based solution of electrostatic and magnetostatic field problems

Abstact Applications of boundary element methods (BEM) to the solution of static field problems in electrical engineering are considered in this paper. The choice of a suitable BEM formulation for electrostatics, steady current flow fields or magnetostatics is discussed from user's point of view. The dense BEM matrix is compressed with an enhanced fast multipole method (FMM) which combines well-known BEM techniques with the FMM approach. An adaptive grouping scheme for problem oriented meshes is presented along with a discussion on the influence of the mesh to the efficiency of the FMM. The computational costs of the FMM algorithm are analyzed for typical problems in practice. Finally, some electrostatic and magnetostatic numerical examples demonstrate the simple usability and the efficiency of the FMM. Communicated by: U. Langer     

The Variable Order Fast Multipole Method for Boundary Integral Equations of the Second Kind

We discuss the variable order Fast Multipole Method (FMM) applied to piecewise constant Galerkin discretizations of boundary integral equations. In this version of the FMM low-order expansions are employed in the finest level and orders are increased in the coarser levels. Two versions will be discussed, the first version computes exact moments, the second is based on approximated moments. When applied to integral equations of the second kind, both versions retain the asymptotic error of the direct method. The complexity estimate of the first version contains a logarithmic term while the second version is O(N) where N is the number of panels.This work was supported by the NSF under contract DMS-0074553     

On a Galerkin boundary node method for potential problems

A Galerkin boundary node method (GBNM), for boundary only analysis of partial differential equations, is discussed in this paper. The GBNM combines an equivalent variational form of a boundary integral equation with the moving least-squares (MLS) approximations for generating the trial and test functions of the variational formulation. In this approach, only a nodal data structure on the boundary of a domain is required, and boundary conditions can be implemented directly and easily despite of the fact that the MLS shape functions lack the delta function property. Formulations of the GBNM using boundary singular integral equations of the second kind for potential problems are developed. The theoretical analysis and numerical results indicate that it is an efficient and accurate numerical method.     

基于FMM和CRFs双层分词模型的研究

中文分词是众多自然语言处理任务的基本工作。该文提出了一个用双层模型进行中文分词的方法。首先在低层利用前向最大匹配算法（FMM）进行粗分词,并将切分结果传至高层;在高层利用CRFs对文本重新进行标注,其中低层的识别结果作为CRFs的一项特征,最后将对每个字的标注结果转换为相应的分词结果。,跟以前单独利用CRF进行分词的模型相比．低层模型的加入对CRFs模型的标注起到了重要的辅助作用。在北京大学标注的1998年1月份的人民日报语料上进行了大量的实验,取得了精确率93．31％,召回车92．75％的切分结果,证明该方法是切实可行的。     

GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method

An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.     

一类高振荡微分方程组的一个对称数值解法

讨论形如（x）＋Ω^2x=g（x）（g（x）=-（（δ）U）/（（δ）x））的一类高振荡微分方程组数值解法构造问题.我们给出了计算该类方程组的一个对称数值解法.并以FPU问题为例进行数值实验,与脉冲法相比较,数值实验结果显示该解法具有较好的能量保守性.     

FMM能效分析及其ASIC可行性评估

对快速多极方法(FMM)进行研究,分析其关键计算任务,并在CPU与DSP上进行验证,得出FMM在不同平台上性能和功耗的量化分析结果,给出基于FMM的多核DSP可重构ASIC结构模型。以可重构硬件FPGA为例,对该模型进行预测,结果证明其在涉及大规模浮点计算时具有一定的能效优势。     

Fredholm积分方程的正则化GMRES算法

利用数值求积公式,对二维第1类Fredholm积分方程进行离散处理,引入正则化GMRES算法,将离散后的积分方程转化为离散适定问题,通过广义极小残余算法得到其数值解。数值模拟结果表明,正则化GMRES算法求解二维第1类Fredholm积分方程计算速度快、精度高。     

An algorithm for velocity calculation in close proximity to body surfaces in panel methods

To model incompressible flow over a body of arbitrary geometry when using vortex methods, it is necessary to construct an irrotational field to impose the impermeability condition at the surface of the object. In order to achieve this impermeability, this paper uses a boundary integral equation based on the single-layer representation for the velocity potential. Specifically, we formulate this exterior Neumann problem in terms of a source/sink boundary integral equation. The solution to this integral equation is then coupled with an interpolation procedure which smoothes the transition between near-wall and interior regimes. We describe the numerical scheme embedding this strategy and discuss its accuracy and efficiency. For validation purposes, we consider the potential and vortical flow over a circular cylinder, for which an analytical solution and the commonly used method of images are available.