A new higher order finite-difference approximation scheme for themethod of lines

A new 5-point and a 7-point nonuniform mesh finite-difference scheme is introduced to approximate the second-derivative operator. The scheme is applied using the method of lines. The necessary interface conditions for the TE and TM fields at an index discontinuity are appropriately included in the derivation. This scheme can model lossy dielectrics as well as metallic layers in a unified way. Numerical results are given for the fundamental TE and TM modes of a high-contrast waveguide and for a metal/dielectric single interface TM surface-plasmon mode showing excellent convergence behavior to the analytical results     

Mixture models with higher order moments

The authors present a novel method for mixed pixel classification where the classification of groups of mixed pixels is achieved by taking into consideration the higher order moments of the distributions of the pure and the mixed classes. The equations expressing the relationship between the higher order moments are used to augment the set of equations that express the relationship between the means only. The authors show that weighting these equations does not make the set of equations available less reliable. As a consequence, the number of equations can be increased and thus more classes than available bands can be identified. The method is exhaustively tested using simulated data and is also applied to real Landsat TM data for which ground data are available     

An accurate broad-band method of moments using higher order basis functions and tree-loop decomposition

A method is presented that combines the low-frequency accuracy of tree-loop decomposition with higher order basis functions to achieve an electric field integral equation based method of moments that is accurate over a wide band of frequencies. In general, the use of higher order divergence-conforming bases introduces more solenoidal degrees of freedom than the standard Rao-Wilton-Glisson (zeroth-order) bases. These solenoidal degrees of freedom are counted and identified, and an efficient method to construct the required higher order loops is presented. Numerical results demonstrate that the technique allows the use of a single mesh to acquire scattering results over a wide band of frequencies using arbitrary order basis functions.     

高阶曲线矢量有限元方法实现及关键问题

针对传统的直线型高阶矢量基函数对曲边界模拟不好的缺点,研究了基于四面体叠层矢量元的高阶曲线建模技术。系统而显式地分析了三维高阶曲线矢量元的实现过程,探讨了实现过程中的一些关键问题。通过分析一个球形谐振腔,系统比较了各种直线或曲线形式的高、低阶矢量元的性能（如计算精度、条件数等）,并将其用于分析不均匀腔体的谐振问题。计算结果表明：采用曲线元对曲线模型进行建模,在不影响计算效率的情况下,可极大地提高计算精度。     

Transient signal detection using higher order moments

The asymptotic performance of transient detection based on higher order moments is theoretically derived, invoking the asymptotic normality of the decision statistics, and a detector based on the third-order absolute moment is proposed. The analysis shows that for a transient duration of less than half the observation window, the proposed detector outperforms the detectors based on the second- and fourth-order moments for a wide range of SNR values. Computer simulations assess the applicability of the theoretical analysis     

A novel algorithm for higher order filtering in DLTS

The problem of enhanced selectivity in DLTS systems is treated on the basis of a multipoint transient analysis (MPA) as an alternative to multichannel filtering. A virtual cascade of time domain filters is utilized as an algorithm for higher-order filtering. Selectivity at both the long time constant and short time constant part of the spectrum is improved simultaneously with an increasing order of the filter using a trivial gating function. A simple transition from the MPA cascade to multichannel cascade filtering is shown. Finally, conditions are specified for making a choice between current or capacitance (charge) transient processing.     

Accurate modelling of anti-resonant dipole antennas using themethod of moments

The authors demonstrate that the difficulties encountered when modelling anti-resonant antennas are primarily due to the conventional variable gap source model which is commonly employed in thin-wire moment method codes. An alternative source model is introduced, for use in analysing this class of antennas, where the essential feature is that the gap width of the feed region remains fixed. The fixed gap model is compared to the variable gap model for both a half-wave dipole, where the variable gap is still a valid source model, and for a full-wave anti-resonant dipole, where the fixed gap source is shown to be superior to the variable gap model     

Singular higher order complete vector bases for finite methods

This paper presents new singular curl- and divergence-conforming vector bases that incorporate the edge conditions. Singular bases complete to arbitrarily high order are described in a unified and consistent manner for curved triangular and quadrilateral elements. The higher order basis functions are obtained as the product of lowest order functions and Silvester-Lagrange interpolatory polynomials with specially arranged arrays of interpolation points. The completeness properties are discussed and these bases are proved to be fully compatible with the standard, high-order regular vector bases used in adjacent elements. The curl (divergence) conforming singular bases guarantee tangential (normal) continuity along the edges of the elements allowing for the discontinuity of normal (tangential) components, adequate modeling of the curl (divergence), and removal of spurious modes (solutions). These singular high-order bases should provide more accurate and efficient numerical solutions of both surface integral and differential problems. Sample numerical results confirm the faster convergence of these bases on wedge problems.     

均匀介质目标高阶矩量法的高效预处理方法

针对均匀介质目标的高阶联合切向积分方程(CTF)迭代求解收敛慢甚至不收敛的问题,提出了一种高效预处理构建方法。通过研究CTF离散方程的矩阵特性,发现矩阵方程中等效电流和等效磁流的两个耦合项具有绝对数值相差很大的特征。利用此特征,提出了先忽略弱耦合项,再用不完全LU分解构造预处理器。数值算例表明:采用此预处理技术的高阶CTF方程在保留CTF方程高精度与稳定性的基础上,具高效性。     

高阶矢量有限元方法实现及关键问题

以二阶三角形矢量元分析均匀无耗波导问题为例，系统而显式地分析了高阶矢量元的实现过程，探讨了实现过程中的一些关键问题。基于基函数分类和单元矩阵分块技术，提出了一种新型的针对高阶矢量元编程的实现方法，可有效地推广到三维情况下任意形式的高阶元。数值实例验证了该方法的可靠性。     

A novel implementation of multilevel fast multipole algorithm for higher order Galerkin's method

A new approach is proposed to reduce the memory requirements of the multilevel fast multipole algorithm (MLFMA) when applied to the higher order Galerkin's method. This approach represents higher order basis functions by a set of point sources such that a matrix-vector multiply is equivalent to calculating the fields at a number of points from given current sources at these points. The MLFMA is then applied to calculate the point-to-point interactions. This permits the use of more levels in MLFMA than applying MLFMA to basis-to-basis interactions directly and, thus, reduces the memory requirements significantly.     

Hierarchal vector basis functions of arbitrary order for triangularand tetrahedral finite elements

New vector finite elements are proposed for electromagnetics. The new elements are triangular or tetrahedral edge elements (tangential vector elements) of arbitrary polynomial order. They are hierarchal, so that different orders can be used together in the same mesh and p-adaption is possible. They provide separate representation of the gradient and rotational parts of the vector field. Explicit formulas are presented for generating the basis functions to arbitrary order. The basis functions can be used directly or after a further stage of partial orthogonalization to improve the matrix conditioning. Matrix assembly for the frequency-domain curl-curl equation is conveniently carried out by means of universal matrices. Application of the new elements to the solution of a parallel-plate waveguide problem demonstrates the expected convergence rate of the phase of the reflection coefficient, for tetrahedral elements to order 4. In particular, the full-order elements have only the same asymptotic convergence rate as elements with a reduced gradient space (such as the Whitney element). However, further tests reveal that the optimum balance of the gradient and rotational components is problem-dependent     

Convergence-optimized, higher order vector finite elements formicrowave simulations

We introduce a general class of higher order parameter-dependent Whitney elements, unlike previous approaches that resulted in specific element definitions. All elements of this kind provide the same solution, but their convergence properties may be significantly different. The most essential fact, though, is the introduction of an optimization procedure, which reveals the existence of an optimal, with respect to convergence, element. The produced second order elements are tested in both two-dimensional (2-D) and three-dimensional (3-D) microwave simulations     

碰撞等离子体的高阶FDTD算法

给出了电磁波在均匀、碰撞等离子体中传播的四阶时间和四阶空间FDTD算法.该算法比Yee氏FDTD算法每一个网格每一维增加一个存储单元,与常规的二阶等离子体FDTD算法相同.由于采用四阶时间和四阶空间近似,因此该算法能有效地减小数字色散误差,其频带宽度比二阶算法的频带宽度更宽.为了验证该高阶算法的正确性,对均匀、碰撞等离子体平板的电磁波反射系数进行了计算,并与解析结果、二阶FDTD计算结果进行了比较,证明了该算法的高效和精确.     

Modelling of industrial conveyorized applicators using higher order vector finite elements.

This paper presents a finite element time domain method for the solution of Maxwell's equations in microwave heating applicators using first and second order vector finite elements. Results are compared with experimental data and it has been shown that second order vector finite elements have many advantages over first order elements. Capitalising on the high accuracy and low computational cost attainable by higher order elements, an industrial conveyor belt system is numerically analyzed.     

Accurate computation of bit error probabilities of band-limited asynchronous DS-CDMA systems using higher order moments

An existing method called the simplified improved Gaussian approximation (SIGA) was previously applied to compute the bit error probabilities (BEPs) of band-limited asynchronous direct sequence code division multiple access (DS-CDMA) systems employing general pulse shaping (IEEE Trans. Commun., vol. 50, p. 656, 2002). The SIGA method uses moments up to the second order and is more accurate than the standard Gaussian approximation (SGA) (IEEE Trans. Commun., vol. 50, p. 656, 2002). In this paper, a new method that uses moments up to the fourth order is proposed for computing the BEP. The method is derived from a five-point Chebyshev interpolation formula and is inherently more accurate than the SIGA. Like the SIGA, the new method requires the evaluation of only closed-form expressions and the error function. The new method achieves higher accuracy with a modest increase in computational complexity.     

Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers

A novel double higher order Galerkin-type method of moments based on higher order geometrical modeling and higher order current modeling is proposed for surface integral equation analysis of combined metallic and dielectric antennas and scatterers of arbitrary shapes. The technique employs generalized curvilinear quadrilaterals of arbitrary geometrical orders for the approximation of geometry (metallic and dielectric surfaces) and hierarchical divergence-conforming polynomial vector basis functions of arbitrary orders for the approximation of electric and magnetic surface currents within the elements. The geometrical orders and current-approximation orders of the elements are entirely independent from each other, and can be combined independently for the best overall performance of the method in different applications. The results obtained by the higher order technique are validated against the analytical solutions and the numerical results obtained by low-order moment-method techniques from literature. The examples show excellent accuracy, flexibility, and efficiency of the new technique at modeling of both current variation and curvature, and demonstrate advantages of large-domain models using curved quadrilaterals of high geometrical orders with basis functions of high current-approximation orders over commonly used small-domain models and low-order techniques. The reduction in the number of unknowns is by an order of magnitude when compared to low-order solutions.     

Identification of cubic systems using higher order moments ofi.i.d. signals

A simple method for estimating the Volterra kernels of cubic systems with a zero-mean i.i.d. input is presented. This method significantly reduces the computational complexity of Volterra kernel estimation compared to the non-i.i.d. and non-Gaussian input case     

A novel OFDM receiver with second order polynomial Nyquist window function

A class of time domain second order polynomial Nyquist window functions and a new receive method are proposed and applied to orthogonal frequency-division multiplexing for reducing frequency offset induced inter-carrier interference (ICI) in the receiver. As far as the delay spread is shorter than the guard interval, we can find a member of the class providing better signal to ICI ratio than the rectangular function and raised cosine function.     

A special higher order finite-element method for scattering by deepcavities

A special higher order finite-element method is presented for the analysis of electromagnetic scattering from a large, deep, and arbitrarily shaped open cavity. This method exploits the unique features of the finite-element equations and, more importantly, the unique features of the problem of scattering by a large and deep cavity. It is designed in such a manner that it uses minimal memory, which is proportional to the maximum cross section of the cavity and independent of the depth of the cavity, and its computation time increases only linearly with the depth of the cavity. Furthermore, it computes the scattered fields for all angles of incidence without requiring significant additional time. The technique is implemented with higher order tetrahedral and mixed-order prism elements, both having curved sides to allow for accurate modeling of arbitrary geometries. Numerical results show that higher order elements yield a remarkably more accurate and efficient solution for scattering by three-dimensional (3-D) cavities. Of the two kinds of element, the mixed-order prism is optimal for the proposed special solver