MEI系数的快速算法

不变性测试方程法已被证明是解决电磁问题的一种有效方法。目前电大尺寸问题中ＭＥＩ系数的计算已成为一个瓶颈。提出了一个快速算法用于加速ＭＥＩ系数的计算,它使用快速多极子方法计算测试子的散射场,使得ＭＥＩ系数的计算速度从Ｏ（Ｎ＾２）变为Ｏ（Ｎ＾１．５Ｌｏｇ２Ｎ）。     

An analytical characterization of the error in the measuredequation of invariance

In previous publications, the authors have numerically shown that the measured equation of invariance (MEI) is not invariant to excitation. The major implication is that an appropriate set of metrons should be selected for each geometry and excitation in question. An argument, however, can be raised against these findings. One can claim that the MEI is indeed invariant, and that any discrepancies are entirely due to the mesh discretization error. The authors disprove this claim by a counterexample. They perform an analytical study of the MEI as applied to a perfectly conducting circular cylinder with a fixed choice of metrons. They then investigate the behavior of the MEI when the electrical radius of the cylinder becomes large and when the nodal separation goes to zero. They prove that even as the MEI residual goes to zero the error in the MEI solution remains finite and cannot be reduced below a certain limit     

Domain-decomposed MEI method for field computation in single andmultiple regions

The domain-decomposed measured equation of invariance (DDMEI) method is proposed for field computation in single and multiple regions. The whole computing domain is partitioned into a cluster of subdomains. For single region problems, this partition splits the computing domain into many subdomains artificially. For multiple regions problems, these subdomains can be taken as those regions separated geometrically. The contribution of sources residing in a subdomain is approximated by a set of sources selected out of these original sources with greatly reduced amounts. The approximation is implemented numerically by the MEI method. The resultant MEI matrices are blocked matrices and each submatrix is highly sparse. Approaches and numerical results are given respectively for the applications of the DDMEI to the scattering of single conducting cylinders, radiation of wire arrays, and capacitance matrix computation for multiconductor transmission lines. The DDMEI proposed in this paper is an improved version of the surface current MEI method (SCMEI). Compared with the SCMEI, the DDMEI improves the sparsity of the MEI matrices and the feasibility of measuring out the MEI coefficients. Furthermore, the DDMEI makes it possible to apply the kind of on-surface MEI methods (OSMEI) to multiple region problems for the first time     

Acceleration of on-surface MEI method by new metrons and FMM for 2-D conducting scattering

A new kind of metron is proposed and rapid integration provided by fast multipole methods (FMM) is implemented to dramatically reduce the CPU time of finding the MEI coefficients in the on-surface measured equation of invariance (OSMEI) method. The numerical example of the scattering of a large conducting elliptical cylinder shows that the computation speed is at least one order of magnitude faster than that of the original OSMEI, where sinusoidal metrons are used, and about 25% faster than that of the FMM, where the iteration method is used.     

An iterative measured equation technique for electromagneticproblems

An iterative measured equation technique (IMET) is presented for a numerical solution of electromagnetic problems. This technique is an extension and improvement of the method of measured equation of invariance (MEI). In this technique, an iterative scheme is designed in such away that a new set of metrons used to generate the measured equations is formed in each iteration based on the solution of the previous iteration. The new metrons are more meaningful in that they converge to the physical quantity of interest such as the surface current density for electrodynamic problems and the surface charge density for electrostatic problems. The IMET offers several advantages over the MEI method because it requires only two mesh layers, resulting in a significant reduction in the memory requirement and computing time. More importantly, it provides a means for a systematic improvement of the accuracy of solution. The IMET is applied successfully to two-dimensional (2-D) electrodynamic and three-dimensional (3-D) electrostatic problems. Numerical results show that the technique is highly accurate and the iterative process converges very quickly, usually within two iterations     

A theoretical and numerical analysis of the measured equation ofinvariance

The measured equation of invariance (MEI) has been previously introduced to efficiently and accurately handle the boundary truncation for finite methods. The present authors give a theoretical analysis that provides several important insights into the capabilities of the MEI. From the numerical study, they can explain why the MEI works better than one would expect. Both the theoretical and the numerical analyses demonstrate that the accuracy of the solution is dependent on the electrical size of the geometry as well as the distance between the mesh boundary and the geometry. From the analysis, the authors propose a new set of metrons that is less sensitive to the excitation than the previously proposed sinusoidal metrons     

Application of discrete periodic wavelets to measured equation ofinvariance

Recently, the wavelet expansions have been applied in field computations. In the frequency domain, the application is focused on the thinning of matrices arising from the method of moment (MoM). The thinning of matrices can best be done by the measured equation of invariance (MEI), which provides sparsity almost without sacrificing accuracy in that the boundary equation it entails is convertible to that of the MoM. The real power of the wavelet expansions is to give high resolution in convolution integrals. High resolution is also needed in the process of finding the MEI coefficients, which are obtained via an integration process almost identical to that of the MoM. In this paper, it is shown that when the fast discrete periodic wavelets (FDPW) are used as metron currents in the MEI method, the resolutions of the MEI coefficients are improved at high-frequency computations or at geometric extremities. The level of sparsity of the MEI is much more favorable than that achievable by the thinning of MoM matrix using the wavelet expansions. The role of FDPW in the MEI happens to be more fitting than its place in the MoM     

MEI系数循环卷积的快速解法

提出了一种用于减少不变量测试方程(MEI)法计算时间的快速算法,循环卷积和快速多极子(FMM)技术(CC-FMM)分别用于不同区域对应的MEI系数,可以加速建立不变量测试方程所需系数的计算.由于循环卷积和FMM的计算效率明显高于直接求和,故整个算法的计算时间明显减少.二维验算实例验证了这种算法的有效性和准确度.     

Comments on “A theoretical and numerical analysis of themeasured equation of invariance”

In the original paper (see ibid., vol.42, no.8, p.1097-1105, 1994), the authors claimed to have found theoretical insights into the measured equations of invariance (MEI) method. Their first insight was a proof that the postulate of invariance was wrong, and their second insight led to the discovery of an optimum set of metrons. Metrons are considered to be “possible” induced current densities due to some unknown incident fields. They also presented a series of computational results to highlight their theories. This article points out the defects in the analyses and conclusions presented by the authors. There are two things in the paper which are basically incorrect. One is that the authors consider a zero in a numerical formulation to be an absolute zero. The other is that they assume the “invariance to excitations” to be the same as the “invariance to metrons”. Based on these assumptions, they have reached conclusions which are actually contradictory to their own calculations. This article shows where the defects of their analyses occur and why their two insights are contradictory to each other     

An iterative algorithm based on the measured equation of invariancefor the scattering analysis of arbitrary multicylinders

It is known that the measured equation of invariance (MEI) is generally valid for outgoing waves just as other absorbing boundary conditions (ABCs). However, for the scattering problem of multicylinders, the scattered field from one cylinder is just the in-going incident wave to other cylinders. So the MEI cannot be directly applied to the scattering problem of multicylinders. In this paper, an iterative algorithm based on the MEI is first proposed for the scattering problems of multicylinders with arbitrary geometry and physical parameters. Each cylinder is coated with several layers of meshes and the MEIs are applied to the truncated mesh boundaries. It has been demonstrated that the MEI can truncate the meshes very close to the surfaces of the cylinders and then results in dramatically savings in memory requirements and computational time. The MEI coefficients of each cylinder can be stored and reused to form the sparse matrices during each iteration procedure as they are independent of excitations. So more central processing unit (CPU) time is saved as the MEI coefficients are calculated only once in the algorithm. The method can be applied to problems of various kinds of multiple cylinders with arbitrary configurations and cross sections. Numerical results for the scattered fields are in good agreement with the data available. Finally, examples are given to show the iterative algorithm applicable to electrically large multicylinders coated with lossy media     

Validity of the measured equation of invariance

The measured equation of invariance (MEI) is derived without any postulates. It is shown that the coefficients of the MEI are invariant to the field of excitation. However, the accuracy of the MEI solution is closely related to the number of nodes in the MEI. Coupling more nodes improves progressively the accuracy of the MEI solution. With increasing nodes, the matrix problem for the determination of the MEI coefficients becomes seriously ill conditioned and generally must be solved using multiple precision arithmetic. The consequences of the ill-conditioning phenomenon are discussed     

时域MEI方法在矩形导体柱散射问题中的应用

本文用时域有限差分法（FDTD）模拟二维矩形导体柱的电磁散射场，采用时域不变性测试方程（MEI）作为吸收边界条件对该散射场进行求解。将所得计算结果与截断边界网格点采用Mur二阶吸收边界条件所得的数值结果相比较，两者吻合很好。结果表明使用时域MEI方法作为吸收边界条件能有效缩短截断边界与物体边界的距离，且能得到足够精确的解。     

Scattering from irregular-edged planar and curved surfaces

An electric field integral equation (EFIE) formulation is used to describe the electromagnetic scattering from finite planar and curved perfect electrical conducting surfaces truncated by an irregular edge. The edge can have an arbitrary form if it satisfies certain differentiability requirements. Similarly, the generating curve describing the surface can be convex, concave, or a combination of both. An edge-dependent entire domain Galerkin expansion is used for the current variation along the surface in the direction of translation. A subdomain expansion is used along the orthogonal direction. The backscatter cross sections obtained from the method of moments are compared with experimental data     

不变性测试方程法在开边界多导体静电系统分析中的应用

在"测试环"概念的基础上,提出了两种确定MEI系数的方法.数值结果表明,利用电偶极子层激励作为测试子和自由空间格林函数作为积分核确定MEI系数的方法,比之其它方法具有更高的精度和明显的优点.分析并总结了数值实验中出现的一些问题,使得对MEI方法的理解更深入了一步.另外,对MEI方法的不稳定性和有效性也做了理论分析.最后,利用本文方法计算了一个较为复杂的微带线参数,得到了满意的结果.     

EM scattering analysis of a ferrite cylinder by a FD-FD technique with an effective absorbing boundary condition and MEI

Electromagnetic scattering problem of an arbitrarily shaped ferrite cylinder is analyzed based on the finite difference-frequency domain(FD-FD) method with an effective numerical absorbing boundary condition (ABC) and the measured equation of invariance (MEI) on the terminated boundary. Compared with the method of moments (MoM), both the numerical ABC presented in this paper and the MEI result in dramatic savings in computing time and memory requirement for electrically large objects due to the sparsity of the finite difference equation. The absorbing characteristic of this numerical ABC is demonstrated numerically. The accuracy, memory needs and CPU time of the FD-FD with the numerical ABC or the MEI and the MoM are compared and then result in some important conclusions. Besides, the RCS of some ferrite cylinders are presented.     

时域MEI方法初探

对时域ＭＥＩ方法进行了初步探索,根据ＭＥＩ方法的基本原理,建立起时域ＭＥＩ方法的一阶吸收边界条件,应用该条件对线源辐射问题的数值实验和研究表明,它可使截断边界离源更近,同时也证实了时域ＭＥＩ方法的可靠性和精确性。     

Electrostatic solution for three-dimensional arbitrarily shapedconducting bodies using finite element and measured equation ofinvariance

Differential equation techniques such as the finite element (FE) and finite difference (FD) have the advantage of sparse system matrices that have relatively small memory requirements for storage and relatively short central processing unit (CPU) time requirements for solving electrostatic problems. However, these techniques do not lend themselves as readily for use in open-region problems as the method of moments (MoM) because they require the discretization of the space surrounding the object where the MoM only requires discretization of the surface of the object. A relatively new mesh truncation method known as the measured equation of invariance (MEI) is investigated augmenting the FE method for the solution of electrostatic problems involving three-dimensional (3-D) arbitrarily shaped conducting objects. This technique allows truncation of the mesh as close as two node layers from the object. The MEI views sparse-matrix numerical techniques as methods of determining the weighting coefficients between neighboring nodes and finds those weights for nodes on the boundary of the mesh by assuming viable charge distributions on the surface of the object and using Green's function to measure the potentials at the nodes. Problems in the implementation of the FE/MEI are discussed and the method is compared against the MoM for a cube and a sphere     

Interpolation, extrapolation, and application of the measuredequation of invariance to scattering by very large cylinders

Using the conventional method of moment (MoM) calculations, a cylinder of circumferential dimension of 100 wavelengths is considered to be large. Using the measured equation of invariance (MEI) approach, a cylinder of 10000 wavelengths is within the storage capacity and numerical tolerance of a workstation. Although, the MEI has greatly reduced the storage and solution time of the matrix, its overhead to generate the matrix elements is about the same order as that of the MoM. When the target is very large, that overhead can be very time consuming. This paper presents an interpolation and extrapolation technique such that the boundary equations of the MEI for high frequencies may be predicted from those of low frequencies. It is demonstrated that in the optical limit the same set of coefficients may be used for all frequencies, which is consistent with the concept of geometric optics where the same rule is applied to all frequencies     

Content Authentication Based on JPEG-to-JPEG Watermarking

A content authentication technique based on JPEG-to-JPEG watermarking is proposed in this paper. In this technique, each 88 block in a JPEG compressed image is first processed by entropy decoding, and then the quantized discrete cosine transform (DCT) is applied to generate DCT coefficients: one DC coefficient and 63 AC coefficients in frequency coefficients. The DCT AC coefficients are used to form zero planes in which the watermark is embedded by a chaotic map. In this way, the watermark information is embedded into JPEG compressed domain, and the output watermarked image is still a JPEG format. The proposed method is especially applicable to content authentication of JPEG image since the quantized coefficients are modified for embedding the watermark and the chaotic system possesses an important property with the high sensitivity on initial values. Experimental results show that the tamper regions are localized accurately when the watermarked JPEG image is maliciously tampered.     

Time-scale analysis of motor unit action potentials

Quantitative analysis in clinical electromyography (EMG) is very desirable because it allows a more standardized, sensitive and specific evaluation of the neurophysiological findings, especially for the assessment of neuromuscular disorders. Following the recent development of computer-aided EMG equipment, different methodologies in the time domain and frequency domain have been followed for quantitative analysis. In this study, the usefulness of the wavelet transform (WT), that provides a linear time-scale representation is investigated, for describing motor unit action potential (MUAP) morphology. The motivation behind the use of the WT is that it provides localized statistical measures (the scalogram) for nonstationary signal analysis. The following four WT's were investigated in analyzing a total of 800 MUAP's recorded from 12 normal subjects, 15 subjects suffering with motor neuron disease, and 13 from myopathy: Daubechies with four and 20 coefficients, Chui (CH), and Battle-Lemarie (BL). The results are summarized as follows: 1) most of the energy of the MUAP signal is distributed among a small number of well-localized (in time) WT coefficients in the region of the main spike, 2) for MUAP signals, we look to the low-frequency coefficients for capturing the average waveshape of the MUAP signal over long durations, and we look to the high-frequency coefficients for locating MUAP spike changes, 3) the Daubechies 4 wavelet, is effective in tracking the transient components of the MUAP signal, 4) the linear spline CH (semiorthogonal) wavelet provides the best MUAP signal approximation by capturing most of the energy in the lowest resolution approximation coefficients, and 5) neural network DY (DY) of Daubechies 4 and BL WT coefficients was in the region of 66%, whereas DY for the empirically determined time domain feature set was 78%. In conclusion, wavelet analysis provides a new way in describing MUAP morphology in the time-frequency plane. This method allows for the fast extraction of localized frequency components, which when combined with time domain analysis into a modular neural network decision support system enhances further the DY to 82.5% aiding the neurophysiologist in the early and accurate diagnosis of neuromuscular disorders.