一种适合FMM法的预处理技术在车载通信系统中的应用

提出了一种针对适合于快速多极子(FMM)近场作用矩阵的不完全LU预条件方法。与传统单纯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,因而可以获得更好的预条件矩阵。利用该预条件技术,收敛更快,计算花费的时间和存储量更少。数值试验表明,此方法是一种适合FMM计算的预条件技术。     

一种有效预条件方法加速FMM分析大型微带阵列

为了加速快速多极子法(FMM)结合离散复镜像法分析大型微带阵列的收敛性,提出了一种有效的预条件方法--不完全LU法(ILU),并测试了几种典型迭代算法结合该预条件方法的效率,讨论了参数选取对迭代效率的影响.数值结果表明:FMM结合ILU预条件方法能够明显提高计算效率.     

快速PO-MoM技术分析电大载体线天线宽带特性

PO-MoM混合方法是研究电大尺寸载体上天线特性的有效方法。在应用PO-MoM分析复杂载体上天线宽频带电磁辐射问题时,由于需要在间隔很小的多个频率点进行填充阻抗矩阵的运算,计算过程耗时多,效率低。本文采用阻抗插值技术,通过构造有理插值函数来快速计算PO-MoM中的阻抗矩阵,并在迭代求解方程过程中采用了一种近场预条件技术,节省了计算时间,提高了计算效率。采用上述快速技术计算了垂直安装于平板的单极子天线和星载螺旋天线的宽带特性,并探讨了阻抗矩阵插值技术实现过程中一些参数的选取的问题。数值结果表明,结合阻抗插值矩阵插值技术并使用预条件技术的PO-MoM可以快速有效地分析大型复杂载体上天线的宽频带特性。     

正则化预条件方法在矩量法中的应用

计算电磁学中矩量法产生的系统矩阵是病态矩阵,使用迭代方法求解时很难收敛,即使采用现有的预条件技术也经常不收敛.本文借用不适定问题求解中的正则化方法的概念,提出采用正则化矩阵作为矩量法中矩阵方程的一个预条件矩阵.这种预条件方法可以直接改善原矩阵的特征值分布,而且不需要额外的空间来存储预条件矩阵.此外,本文提出通过正则化矩阵方程的L曲线的二阶导数的最大值点来确定正则化参数,使得预条件矩阵方程求解的效率最高.数值实验表明,对于高阶矩量法求解电场积分方程或者磁场积分方程时分别产生的矩阵方程,采用常见的预条件迭代方法求解时收敛很慢,但是采用本文的预条件迭代方法却可以较快地收敛.     

“邻居单元”为基础的预条件方法及其应用

该文提出了一种具有物理意义的预条件方法--"邻居单元"为基础的预条件方法。该方法充分考虑了矩阵元素中的"主要"信息量,可以有效加快迭代收敛速度。在构造预条件因子时,采用从目标的"几何结构剖分"出发,而不是从"矩阵元素"出发确定"基权函数之间的作用量关系",这样保证了构造预条件矩阵的计算复杂度仅为O(N)。作为实例,该文将这种预条件方法与共轭梯度方法结合应用于矩量法基站天线分析所得方程的求解,数值结果表明了该文方法的有效性。     

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。     

一种基于高阶矢量基函数的叠层预条件技术

基于六面体的高阶叠层基函数,提出了一种新颖的构造预条件矩阵的方法.该方法基于叠层基函数特有的嵌套性质,利用特殊的编号策略,将由有限元方法导致的系数矩阵分成块矩阵的形式,最后由不完全LU分解(ILU)导出近似的预条件矩阵.结合该预条件技术,发展了一种叠层预条件-GMRES算法,并将该预条件算法用于加速三维腔体散射的矢量有限元/边界积分(FE-BI)矩阵方程的迭代求解,讨论了该预条件算法中块矩阵ILU分解截断门限T_dr对算法的影响.     

求解复杂载体天线辐射问题的近场预条件技术

提出了一种近场预条件技术与LDU分解法相结合的新技术,用于加速矩量法(MoM)分析复杂载体上线天线辐射问题中线性方程组的迭代求解.通过LDU分解可将系数矩阵中表示载体上单元相互作用的具有对角占优特性的子阵分离出来,构造一个矩阵分解形式的预条件阵.结合广义最小留数(GMRES)法,分别对装载在两个简单形体和一架大型飞机模型上的线天线的辐射问题进行了求解.数值结果表明,该方法可大大加快线性方程组迭代求解的收敛速度,提高分析计算效率.     

一种综合处理光栅矢量衍射的新方法

理论上将Waterman -Rayleigh方法 (WRM) ,傅立叶模方法 (FMM)和坐标变换法 (CM)巧妙结合 ,吸收了三者各自处理多分层光栅的优点 ,摒弃了各自的缺点 ,简化了理论推导。采用WRM方法的形式来表示电磁场 ,以便省去对本征值和本征矢的数值计算时间 ;采用FMM对物理量作矩阵表述 ,以便实现理论推导的简洁性 ,规范性 ;采用CM的坐标变换 ,以便简化对边界条件的匹配 ;在作Fourier展开时采用“逆规则” ,以保持方法的快速收敛性 ;在对多分层光栅的递推计算中 ,采用反射透射系数阵算法 (RTCM) ,以便克服由于层与层之间厚度变大所带来的数值不稳定性 ,同时提高计算速度。总之 ,这种综合处理光栅问题的方法不仅物理概念清晰 ,计算简洁 ,速度快 ,而且准确性 ,稳定性和收敛性均令人满意。     

大型波导缝隙阵辐射特性的快速分析

针对矩量法分析大型波导缝隙阵时矩阵填充和方程求解速度慢的问题,本文首先给出了负载均衡的并行计算方案,解决了阻抗矩阵填充非常慢这一困难,接着提出了一种新的 —"缝隙邻居"预条件方法,因其具有从物理上将基函数之间的近场作用充分考虑到预条件矩阵中的优点,故可将典型共轭梯度法求解矩量法分析缝隙阵所得矩阵方程的收敛速度提高了约一个数量级,从而实现了大型缝隙阵列的快速仿真.数值实例表明本文方法的高效性和准确性.     

有耗半空间环境中导体目标电磁散射的快速分析

应用快速多极子方法求解有耗半空间环境中任意三维金属体的雷达散射特性.对于基函数与测试函数的近场组作用,我们用离散复镜像法严格处理半空间并矢格林函数.在处理远场区时,我们利用实镜像源和反射系数近似计算交界面处远场的作用.通过位于有耗半空间三面角反射器、立方体证明了方法的正确性和有效性.另外,将多分辨预处理器和快速多极子方法结合使得矩阵求解器的迭代次数和计算时间减少数倍.     

Reduced-order preconditioning for bidomain simulations

Simulations of the bidomain equations involve solving large, sparse, linear systems of the form Ax = b. Being an initial value problems, it is solved at every time step. Therefore, efficient solvers are essential to keep simulations tractable. Iterative solvers, especially the preconditioned conjugate gradient (PCG) method, are attractive since memory demands are minimized compared to direct methods, albeit at the cost of solution speed. However, a proper preconditioner can drastically speed up the solution process by reducing the number of iterations. In this paper, a novel preconditioner for the PCG method based on system order reduction using the Arnoldi method (A-PCG) is proposed. Large order systems, generated during cardiac bidomain simulations employing a finite element method formulation, are solved with the A-PCG method. Its performance is compared with incomplete LU (ILU) preconditioning. Results indicate that the A-PCG estimates an approximate solution considerably faster than the ILU, often within a single iteration. To reduce the computational demands in terms of memory and run time, the use of a cascaded preconditioner was suggested. The A-PCG was applied to quickly obtain an approximate solution, and subsequently a cheap iterative method such as successive overrelaxation (SOR) is applied to further refine the solution to arrive at a desired accuracy. The memory requirements are less than those of direct LU but more than ILU method. The proposed scheme is shown to yield significant speedups when solving time evolving systems.     

Parallel multigrid preconditioner for the cardiac bidomain model

The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue but are computationally expensive, limiting the size of the problem which can be modeled. The purpose of this study is to determine more efficient ways to solve the elliptic portion of the bidomain equations, the most computationally expensive part of the computation. Specifically, we assessed the performance of a parallel multigrid (MG) preconditioner for a conjugate gradient solver. We employed an operator splitting technique, dividing the computation in a parabolic equation, an elliptical equation, and a nonlinear system of ordinary differential equations at each time step. The elliptic equation was solved by the preconditioned conjugate gradient method, and the traditional block incomplete LU parallel preconditioner (ILU) was compared to MG. Execution time was minimized for each preconditioner by adjusting the fill-in factor for ILU, and by choosing the optimal number of levels for MG. The parallel implementation was based on the PETSc library and we report results for up to 16 nodes on a distributed cluster, for two and three dimensional simulations. A direct solver was also available to compare results for single processor runs. MG was found to solve the system in one third of the time required by ILU but required about 40% more memory. Thus, MG offered an attractive tradeoff between memory usage and speed, since its performance lay between those of the classic iterative methods (slow and low memory consumption) and direct methods (fast and high memory consumption). Results suggest the MG preconditioner is well suited for quickly and accurately solving the bidomain equations.     

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.     

Accurate numerical modeling of the TARA reflector system

The radiation pattern of the large parabolic reflectors of the Transportable Atmospheric RAdar system (TARA), developed at Delft University of Technology, has been accurately simulated. The electric field integral equation (EFIE) formulation has been applied to a model of the reflectors including the feed housing and supporting struts, discretised using the method of moments. Because the problem is electrically large (the reflector has a diameter of 33/spl lambda/) and nonsymmetrical, this lead to a badly conditioned linear system of approximately half a million unknowns. In order to solve this system, an iterative solver (generalized minimum residual method) was used, in combination with the multilevel fast multipole method. Because of the bad conditioning, the system could only be solved by using a huge preconditioner. A new block-incomplete LU preconditioner (ILU) algorithm has been employed to allow for efficient out-of-computer core memory preconditioning.     

Algebraic multigrid preconditioner for homogeneous scatterers in electromagnetics

Electromagnetic wave scattering from large and complex bodies is currently the most challenging problem in computational electromagnetics. There is an increasing need for more efficient algorithms with reduced computational complexity and memory requirements. In this work we solve the problem of electromagnetic wave scattering involving three-dimensional, homogeneous, arbitrarily shaped dielectric objects. The fast multipole method (FMM) is used along with the algebraic multigrid (AMG) method, that is employed as a preconditioner, in order to accelerate the convergence rate of the Krylov iterations. Our experimental results suggest much faster convergence compared to the non preconditioned FMM, and hence significant reduction to the overall computation time.     

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