一种新型针对快速多极子法(FMM)的预条件技术

提出了一种针对FMM近场作用矩阵块的不完全LU预条件方法。和传统单纯依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，因而可获得性能更好的预条件矩阵。利用该项预条件技术，迭代过程变得更健壮，而且收敛也更快，计算花费的时间也更少。数值实验表明：这种基于双丢弃准则的ILUT预条件技术，是一种非常适合FMM计算的预条件处理方法。     

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。     

基于高阶叠层基函数的加速迭代求解方法

研究了高阶叠层矢量基函数的尺度因子对迭代法求解矩阵方程收敛性的影响,选择了可以有效降低矩阵条件数的尺度因子;在此基础上,详细阐述了求解基于高阶叠层矢量基函数阻抗矩阵方程的叠层共轭梯度方法(HCGM),并从理论上分析了叠层共轭梯度算法的收敛性能.通过计算实例表明,与共轭梯度方法(CGM)相比.使用HCGM可以大幅度减少矩阵方程的迭代求解时间.     

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.     

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。     

高阶FE-BI方法及一种新型的预条件技术

将基于六面体网格的高阶矢量基函数(higher order vector basis function)引入到矢量有限元-边界积分(FE-BI)混合方法中,用于建模带有深腔和狭长缝隙结构三维目标的电磁散射特性;提出了一种新型的预条件技术,用于加速FE-BI系统的迭代求解;给出了结合该预条件技术的GMRES方法求解腔体电磁散射的算例;数值结果证明了高阶FE-BI方法相对于低阶FE-BI方法的优势以及新型预条件技术的有效性.     

一种高阶矩量法迭代求解的预处理技术

频域高阶矩量法越来越多地用于求解目标散射问题.但高阶矩量法得到的矩阵方程中,系数矩阵条件数较差,并且一般为非对角占优阵,通常用计算效率较低的直接方法求解.本文针对叠层高阶基函数的特点,提出了一种函数空间域分解的加性Schwarz预处理技术.通过数值计算,给出了最优分解方案,并数值验证了预处理技术的有效性.     

基于两阶段的毫米波大规模MIMO低复杂度混合预编码算法

针对现有基于矩阵分解的混合预编码算法信道容量有损和算法复杂度高的问题,本文提出了一种基于两阶段的低复杂度混合预编码算法.该算法分为获取最优全数字预编码器和求解混合预编码器两部分.首先,本文联合奇异值分解(Singular Value Decomposition,SVD)与注水算法以容量无损的要求设计最优全数字预编码矩阵.其次,为了降低搜索超完备矩阵列的复杂度,提出两阶段混合预编码(Two?Stage Hybrid Precoding,TS?HP)算法求解混合预编码矩阵.第一阶段,根据天线阵列响应矩阵的相关性获取模拟预编码矩阵备选集;第二阶段,利用贪婪搜索对备选集进行搜索构建混合预编码矩阵.仿真结果表明,所提算法能够有效改善系统性能,降低复杂度.     

金属目标快速分析的不完全LU预处理技术

研究了一种用于改善金属目标快速计算迭代收敛特性的预处理技术.采用自适应积分快速算法(AIM)快速精确分析任意结构金属目标的电磁散射特性,着重探讨了运用不完全LU分解方法(ILU)来加速AIM算法的迭代收敛过程的技术.快速算法结合ILU分解技术极大地提高了金属目标电磁特性的分析计算速度.     

毫米波大规模MIMO系统中低复杂度混合预编码方法

针对毫米波大规模多输入多输出(MIMO)系统混合预编码方案设计的难点,提出了一种低复杂度混合预编码方法。首先基于奇异值分解,构造初始射频(RF)预编码矩阵,然后构造数字预编码矩阵。进而将残差矩阵最大左奇异矢量构造的矢量添加到RF矩阵的最后一列,以更新初始RF矩阵。经过多次迭代,从而形成最终RF预编码矩阵。最后基于最小二乘准则设计数字预编码矩阵。理论分析和仿真结果表明,相比于基于正交匹配追踪(OMP)算法的混合预编码设计方法,该方法在计算复杂度大幅下降的同时,其性能远远优于基于OMP算法的混合预编码方法,同时在数据流数相对较小时,其性能接近最优的全数字预编码设计方法。     

A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering

A highly effective preconditioner is presented for solving the system of equations obtained from the application of the hybrid finite element-boundary integral (FE-BI) method to three-dimensional (3-D) electromagnetic scattering problems. Different from widely used algebraic preconditioners, the proposed one is based on a physical approximation and is constructed from the finite element method (FEM) using an absorbing boundary condition (ABC) on the truncation boundary. It is shown that the large eigenvalues of the finite element (FE)-ABC system are similar to those of the FE-BI system. Hence, the preconditioned system has a spectrum distribution clustered around 1 in the complex plane. Consequently, when a Krylov subspace based method is employed to solve the preconditioned system, the convergence can be greatly accelerated. Numerical results show that the proposed preconditioner can improve the convergence of an iterative solution by approximately two orders of magnitude for large problems.     

Scattering analysis of a large body with deep cavities

A numerical scheme is presented for simulating electromagnetic scattering from a large and arbitrarily shaped body, coated with inhomogeneous composite materials, with large and deep cavities. This numerical scheme employs the higher order vector finite-element method (FEM) to discretize the fields inside the cavities and coatings and the higher order boundary integral (BI) method to terminate the FEM computational domain. A highly efficient special solver is designed to eliminate the unknowns inside the cavities, which yields a computed relation (CR) matrix over the cavity's aperture between the tangential electric and magnetic fields. This CR matrix is then combined with the finite element-boundary integral (FE-BI) matrix equation to form a complete linear system for the discrete fields everywhere in the computational domain. The resulting system is solved iteratively using a novel preconditioner derived by replacing the BI with a corresponding absorbing boundary condition (ABC).     

Numerical Simulation of BOR scattering and radiation using a higher order FEM

Numerical simulations of body-of-revolution geometries for scattering and radiation problems are presented. The formulation consists of a finite element-boundary integral (FE-BI) method which is based on a finite element method that uses higher order nodal-based scalar basis functions for the azimuthal field component and higher order edge-based vector basis functions for the transverse field. This formulation, when combined with a symmetric FE-BI hybridization scheme, yields a final system of equations that is more accurate than earlier first-order formulations. Numerical examples are given to demonstrate the accuracy and capabilities of the higher order solution.     

A fast time-domain finite element-boundary integral method forelectromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme     

Efficient Calculation of Interior Scattering From Large Three-Dimensional PEC Cavities

Higher order finite element-boundary integral (FE-BI) method is a powerful tool to model the electromagnetic (EM) scattering from three-dimensional large, deep, and arbitrarily-shaped cavities. To further understand the higher order FE-BI method and its applications to the modeling of interior scattering from very large practical perfect electric conductor (PEC) cavity structures, two aspects will be discussed in this paper. The first is on the development of a new integration method to accurately handle singular integrals in calculating BI matrix elements resulted from higher order basis functions defined on higher order elements. The second is on the numerical and experimental verifications of the higher order FE-BI code developed and its applications to the study of the effects of cavity shape, termination and aperture coupling on the interior scattering from large PEC cavities     

有限差分法解电磁场方程的共轭梯度法三角阵预处理器

通过考察电磁场微分方程经非均匀网格离散后的有限差分方程组矩阵,建立了函数偏微分运算与离散向量矩阵相乘运算的对应关系,给出了差分方程组矩阵对应于微分算子的分解式,并据此提出了共轭梯度法的三角阵预处理器。此外,还提出了对不同的边界条件、求解域内部边界、介质分界面和时谐场方程的处理技术以便应用该预处理器。数值计算结果验证了本文算法的正确性,展示了其十分明显的加速收敛效果,表明了本文算法有线性的存储复杂度和几乎线性的计算复杂度,可有较广泛的应用。本文中将算子细节和矩阵细节对应的基本思想对构造其它高效预处理器具有借鉴作用。     

An efficient preconditioner for electromagnetic integral equations using predefined wavelet packet basis

An approximate-inverse preconditioner based on the predefined wavelet packet (PWP) basis is proposed for the fast iterative solution of electromagnetic integral equations. The PWP basis is designed to achieve a sparse representation of the moment matrix and the preconditioner is constructed by inverting the block-diagonal approximation of the PWP-based moment matrix and transforming the results into the space domain. Numerical results show that the PWP preconditioner is effective in accelerating the convergence rate of iterative solution to moment equations. It is also demonstrated that by properly designing the block-diagonal matrix and computing the matrix elements, the total computational complexity and memory costs for the preconditioner can be kept to O(NlogN).     

结合高阶矢量FE/BI方法的快速WCAWE计算

将矢量有限元/边界积分混合方法(FE/BI)用于背腔式贴片天线的输入阻抗建模,在FE/BI方法中,采用基于六面体网格(hexahedron)的高阶矢量基函数(higher order vector basis functions)展开未知场分量;结合高阶矢量FE/BI,采用最近发展起来的WCAWE技术(Well-Conditioned Asymptotic Waveform Evaluation)实现了贴片天线输入阻抗的快速计算;WCAWE技术通过正交化的方式获得低阶模型,这种方式避免了Arnoldi等子空间技术增加矩阵尺度的缺点,同时也确保具有比传统的AWE更好的频带展宽特性;关于输入阻抗计算的数值结果将证明WCAWE技术的优势.     

Finite element modeling and multigrid preconditioner using adaptive triangular meshes

The letter describes a finite element method (FEM) using adaptive triangular meshes for the modeling of microwave devices. A robust preconditioning technique is provided for the fast solution of the resultant FEM matrix equations. The proposed preconditioner is based on a multigrid scheme for the vector-scalar potential FE formulation of the electromagnetic problem. Numerical experiments demonstrate its superior numerical convergence.