An effective wavelet matrix transform approach for efficientsolutions of electromagnetic integral equations

An effective numerical method based on wavelet matrix transforms for efficient solution of electromagnetic (EM) integral equations is proposed. Using the wavelet matrix transform produces highly sparse moment matrices which can be solved efficiently. A fast construction method for various orthonormal or nonorthonormal wavelet basis matrices is also given. It has been found that using nonsimilarity wavelet matrix transforms such as nonsimilarity nonorthonormal cardinal spline wavelet (NSNCSW) transform, one can obtain a much higher compression rate and much better accuracy of the approximate solutions than using similarity wavelet transforms such as Daubechies' (1992) orthonormal wavelet (DOW) transform. Numerical examples are given to show the validity and effectiveness of the method     

A hybrid wavelet expansion and boundary element analysis ofelectromagnetic scattering from conducting objects

A new wavelet approach is presented for treating the two-dimensional electromagnetic scattering problems over curved computation domains. The wavelet expansion method, in combination with the boundary element method (BEM), is applied to solve the integral equation for the unknown surface current. The unknown surface current is expanded in terms of a basis derived from a periodic, orthogonal wavelet in interval [0, 1]. The geometrical representation of the BEM is employed to establish the map between the curved computation domain and the interval [0, 1]. This technique exhibits the advantages of both the wavelet expansion method and the boundary element method: sparse matrix system and accurately modeling of curved surfaces. Comparisons of the results from the new technique with the moment method solutions, the analytical solutions or the data in previous publications are provided. Good agreements are observed     

Analysis of electromagnetic scattering from conducting bodies ofrevolution using orthogonal wavelet expansions

The wavelet expansion method has been extended to study the electromagnetic scattering from conducting bodies of revolution. The magnetic field integral equation (MFIE) is solved by this approach. By expanding the induced surface currents in terms of Fourier series of uncoupled azimuthal cylindrical modes, a simplified MFIE is attained for each unknown mode current that varies along the curved profile of the scatterer. By applying the boundary element method (BEM), the curved profile is mapped into the definition domain of the orthogonal wavelets on the interval. The unknown mode currents are then expressed using multiscale wavelet expansions. The simplified MFIE is converted into a sparse, multilevel matrix equation by the Galerkin method. Numerical examples are provided to illustrate the merits of this wavelet approach     

An efficient solver for the three-dimensional capacitance of theinterconnects in high speed digital circuit by the multiresolutionmethod of moments

The computation of the equivalent capacitances for three-dimensional (3-D) interconnects features large memory usage and long computing time. In this paper, a matrix sparsification approach based on multiresolution representation is applied with the method of moments (MoM) to calculate 3-D capacitances of interconnects in a layered media. Instead of direct expansion of the charge distribution by the orthogonal wavelet basis functions, the large full matrix resulting from discretization of the integral equations is taken as a discrete image and sparsified by two-dimensional (2-D) multiresolution representations. The inverse of the obtained sparse matrix is efficiently implemented by Schultz's iterative approach. Several numerical examples are given and the results obtained show that the proposed method significantly sparsifies the matrix equation and the capacitance parameters computed by the matrix equation with high sparsity agree well with the results of other reports and those computed by an established capacitance extractor FASTCAP     

A finite-element-boundary integral formulation for scattering bythree-dimensional cavity-backed apertures

A novel numerical technique is proposed for the electromagnetic characterization of the scattering by a three-dimensional cavity-backed aperture in an infinite ground plane. The technique combines the finite element and boundary integral methods to formulate a system of equations for the solution of the aperture fields and those inside the cavity. Specifically, the finite element method is used to formulate the fields in the cavity region, and the boundary integral approach is used in conjunction with the equivalence principle to represent the fields above the ground plane. Unlike traditional approaches, the proposed technique does not require a knowledge of the cavity's Green's function and is, therefore, applicable to arbitrary shape depressions and material fillings. Furthermore, the proposed formulation leads to a system having a partly full and partly sparse as well as symmetric and banded matrix which can be solved efficiently using special algorithms     

基于STFT与G函数相结合的短波DFH跳检测方法

差分跳频利用频率的跳变携带信息,只要正确检测出每跳的频率,就可以恢复出信息.本文提出一种基于STFT的跳检测方法,并与G函数相结合来分析短波DFH信号在每跳时间间隔内的频率特性,以检测可能的跳频率.仿真结果表明,在短波信道几种可能的情况下,检测效果良好.     

位积分方程组矩量法用于精确计算非均匀介质柱的电磁散射

位积分方程组的主要特点是以电磁位为未知函数,这些未知函数在具有不同电磁参数的介质分界面处是连续的,因而在矩量法的实现过程中能够非常方便地应用高阶插值基函数来展开未知函数,以便获得高精度的解。但是,经典的点匹配方案使该模型的数值稳定性较差。本文用位积分方程组矩量法模型计算任意截面非均匀介质柱的电磁散射,采用三角形离散方案和高阶插值基函数,在测试过程中应用新提出的测试方法,克服了原位方程组矩量法模型的数值不稳定性。对矩量法矩阵中自阻抗元素的奇异性处理方法也作了详细介绍。文中提供的数值结果表明,该方法是精确、稳定的。     

电大尺寸开口腔体电磁散射的子结构法研究

将子结构法与矢量有限元法相结合对无限大接地的三维开口腔体的电磁散射特性进行分析.将原尺寸较大的腔体分解成若干个不重叠的子腔体,在各子腔体内应用矢量有限元法进行分析,在原腔体开口面应用边界积分方程描述.通过求解容量矩阵获得子腔体之间连接边界上的场值,可以快速获得腔体开口面上的场值,极大地减少了存储量和计算量,易于对电大尺寸腔体的电磁散射问题进行分析.数值算例验证了该方法的准确性和高效性.     

A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

基于频域广义传输矩阵方法的电磁散射特性分析

多尺度复杂电子系统的电磁场问题难以用单一的计算电磁学方法进行高效数值计算.基于区域分解方法和惠更斯等效原理，提出了频域广义传输矩阵（generalized transition matrix，GTM）方法:将系统分解为多个子模块，通过电场积分方程（electric field integreal equation，EFIE）把各个子模块的电磁特性进行提炼，再考虑所有子模块之间的电磁耦合，计算系统整体电磁场分布.GTM方法把多尺度问题转化为尺度相对比较单一的问题进行处理，在分析各种复合结构、非均匀各向异性介质、大型相控阵天线等电磁散射特性时，提供了灵活的解决方案.论文给出了GTM在手征介质、开口腔体以及Vivaldi相控阵天线电磁特性分析中的应用算例，当未知量个数压缩到原来的十分之一时，GTM计算结果与直接用矩量法（methed of moment，MoM）求解的计算结果非常吻合.GTM可以简洁地表示目标问题的电磁散射特征，与传统MoM相比，大幅度减少了基函数的数量，具有较高的计算精度和效率.     

小波矩量法计算导电平面上的三维腔体散射

该文采用小波矩量法求解导电平面上的三维腔体散射,利用小波变换稀疏化矩量矩阵,加速其求逆,减少了腔体散射的总体计算时间。通过具体的算例,表明小波矩量法在计算三维散射问题中是非常有效的。     

线天线的小波矩阵变换法求解

本文研究天线的小波矩阵变换法求解。首先采用三角插值基函数和线天线的一种精确计算模型,利用矩量法得到矩阵方程,然后通过Daubechies离散小波变换进行快速求解。计算结果表明,该方法能够使阻抗矩阵稀疏化,从而提高了求解速度。     

Generalized admittance matrix for a slotted parallel-platewaveguide

An integral equation for the slot electric field in transverse magnetic (TM) scattering and radiation by a slotted parallel-plate waveguide is solved using the moment method. By using piecewise sinusoidal functions for expansion and testing in the moment-method technique, a generalized admittance matrix associated with the slot is obtained in functional form as opposed to numerical integration     

A fast higher-order time-domain finite element-boundary integral method for 3-D electromagnetic scattering analysis

A novel hybrid time-domain finite element-boundary integral method for analyzing three-dimensional (3-D) electromagnetic scattering phenomena is presented. The method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes. To accurately represent the unknown fields, the scheme employs higher-order vector basis functions defined on curvilinear tetrahedral elements. To handle problems involving electrically large objects, the multilevel plane-wave time-domain algorithm is used to accelerate the evaluation of the boundary integrals. Numerical results demonstrate the accuracy and versatility of the proposed scheme.     

三维目标电磁散射矢量有限元/边界元法的公式研究

研究应用于三维目标电磁散射分析的矢量有限元/边界元混合方法不同公式.分析表明,混合公式系统矩阵的条件数随边界元采用不同公式有很大差异,从而导致混合公式的稳定性有很大不同.并讨论了混合方法中边界元部分的单一检验基函数方法和组合检验基函数方法.认为组合检验基函数方法仍可被视为单一检验基函数方法;通过比较边界元部分使用单一检验基函数法和组合检验基函数法时所得计算结果,纠正了只有使用组合检验基函数,有限元/边界元混合方法才能得到精确结果的结论.综合考虑计算结果可靠性、精度及对内部谐振的免疫力等因素,给出了所推荐使用的有限元/边界元混合方法公式.     

多层递推小波算法及其在计算电磁学中的应用

本文给出了一种快速的多层递推小波算法,它能有效地求解由小波展开而获得的稀疏矩阵方程,这种算法利用小波展开的阻抗矩阵的多分辨率表示,将原来的稀疏矩阵方程转化为多个小型矩阵方程进行求解,从而节省求解方程的时间.在本文中,我们以求解二维散射问题为例,将这种算法用于计算电磁学中,数值结果表明该算法比通常的小波算法更快速有效.     

带有腔体或槽缝的电大尺寸目标电磁散射特性分析

本文提出了一种新的混合方法—FEM/PO-PTD法,应用于分析计算带有腔体或槽缝的电大尺寸复杂目标电磁散射问题.在该方法中,采用基于棱边的有限元法(edge-based FEM)为低频方法,物理光学法(PO)与物理绕射理论(PTD)为高频方法,通过耦合技术将两者结合在一起.为了验证该方法的准确性,本文首先将其应用于三维无穷接地开口腔体的电磁散射特性分析,计算结果与有关文献的数据一致性很好.在此基础上,给出了几种不同介质填充的三维开口腔体和带有槽缝的三维有限尺寸导体柱雷达散射截面的计算曲线,对分析有关工程问题有指导意义.理论分析与计算结果表明,本文提出的混合方法与其它计算同类问题的方法相比,能节省计算机存储单元、提高计算速度.     

Scattering and radiation analysis of three-dimensional cavityarrays via a hybrid finite-element method

A hybrid numerical technique is presented for a characterization of the scattering and radiation properties of three-dimensional cavity arrays recessed in a ground plane. The technique combines the finite-element and boundary-integral methods and invokes Floquet's representation to formulate a system of equations for the fields at the apertures and those inside the cavities. The system is solved via the conjugate-gradient method in conjunction with the fast Fourier transform thus achieving an O(N) storage requirement. By virtue of the finite-element method, the proposed technique is applicable to periodic arrays comprised of cavities having arbitrary shape and filled with inhomogeneous dielectrics. Several numerical results are presented, along with new measured data, which demonstrate the validity, efficiency, and capability of the technique     

区域分裂法及其在三维散射中的应用

基于区域分裂（ＤＤＭ）和频域有限差分（ＦＤＦＤ）提出了一种分析三维散射问题的精确高效算法。用区域分裂法可以把原问题分解成若干子问题,可以大大缩小稀疏矩阵的规模,使得求解大尺寸三维散射问题成为可能。文中首先在小尺寸下计算了三维立体柱的散射特性,并和没有进行区域分裂时的ＦＤＦＤ法进行了对比,验证了本算法的正确性;然后又计算了尺寸比较大的三维矩形柱的散射特性,验证了它的高效性。     

Finite-difference analysis of dielectric-loaded cavities using thesimultaneous iteration of the power method with the Chebyshevacceleration technique

A numerical procedure using the finite-difference technique, simultaneous iteration based on the power method, and the Chebyshev-polynomial preconditioning is proposed to analyze dielectric-loaded cavities. The merit of this method is that no matrix inversions are invoked and the convergence rate of the power method is greatly accelerated by the preconditioning. The TE, TM, and hybrid modes in axisymmetrical cavities loaded with a rod or ring dielectric resonator are analyzed. For the hybrid modes, an H_r-H_z formulation is proposed. Accurate numerical results are obtained efficiently and no spurious solutions are found by the present method