Microwave modeling and parameter extraction method for multilayer on‐chip inductors

A new equivalent circuit model for 3D multilayer on‐chip inductors based on physical principles is presented in this article. The model consists of multiple elementary cells, and every cell in the distributed model represents a single stacked inductor. The model also takes into account the distributed effect of the via‐hole with feedline which is used to connect the test pad to the lowest mental layer. A parameter‐extraction approach for proposed model which combines the analytical approach and empirical optimization procedure is investigated. Good agreement is obtained between simulated and measured results for a six metal layers on‐chip inductor on silicon in the frequency range of 50 MHz to 20 GHz. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

残缺区间型矩阵的残缺元计算及其排序新方法

研究了残缺区间数互补判断矩阵的残缺元计算和排序方法问题。通过引入随机残缺互补判断矩阵的概念,定义了残缺区间数互补判断矩阵的一致性指标,并且在满意一致性下利用构建的最优化模型,计算出残缺区间数的具体数值,在基础上结合Q型聚类和灰色关联度给出了残缺区间数互补判断矩阵的排序新方法。通过算例验证了该方法的可行性和有效性。     

Fabrication of X-rays mask with carbon membrane for diffraction gratings

We have produced diffraction gratings for obtaining high resolution X-ray phase imaging, such as X-ray Talbot interferometer. These diffraction gratings were required to have a fine, high accuracy, high aspect ratio structure. Therefore, we decided to use the X-rays lithography technique that used synchrotron radiation of the directivity for a manufacture process. The accuracy of the completed structure depends largely on the accuracy of the X-ray mask. In our group, a resin material is conventionally used for the membrane of large X-ray masks. However, X-ray masks comprising a resin membrane have the disadvantage that, after several cycles of X-ray exposure, they crease and sag due to X-ray-derived heat. As a substitute for the conventional resin membrane, we experimentally fabricated a new X-ray mask using a carbon wafer membrane. The newly fabricated X-ray mask was subjected to X-ray exposure experiment. We succeeded in making the structure body which was almost shape. And the experimental results verified that the new mask did not deteriorate even when used repeatedly, demonstrating that it was highly durable.     

Application of the incomplete Cholesky factorization preconditioned Krylov subspace method to the vector finite element method for 3-D electromagnetic scattering problems

The incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method.     

A discontinuous Galerkin method for the wave equation

We present a new discontinuous Galerkin method for solving the second-order wave equation using the standard continuous finite element method in space and a discontinuous method in time directly applied to second-order ode systems. We prove several optimal a priori error estimates in space–time norms for this new method and show that it can be more efficient than existing methods. We also write the leading term of the local discretization error in terms of Lobatto polynomials in space and Jacobi polynomials in time which leads to superconvergence points on each space–time cell. We discuss how to apply our results to construct efficient and asymptotically exact a posteriori estimates for space–time discretization errors. Numerical results are in agreement with theory.     

面向方面的信息系统建模方法及应用研究

随着面向对象软件开发技术的不断发展以及软件规模的不断扩大,系统地分析和设计变得日益复杂。软件开发过程中很难利用现有的编程技术（如面向对象编程、面向过程编程）对横切系统多个模块的关注点进行鉴别、理解和模块化。为解决面向对象开发方法中的耦合性较高、可重用性较低和代码分散等问题,将面向方面的编程思想引人到系统分析和设计阶段,提出了一种面向方面的信息系统建模方法。     

A B-spline Galerkin method for the Dirac equation

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y^″=−λ²y, that can also be written as a pair of first-order equations y^′=λz, z^′=−λy. Expanding both y(r) and z(r) in the Bk basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the Bk basis and z(r) in the dBk/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method (Bk,Bk±1) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.     

A wavelet Galerkin method for the stokes equations

The purpose of this paper is to investigate Galerkin schemes for the Stokes equations based on a suitably adapted multiresolution analysis. In particular, it will be shown that techniques developed in connection with shift-invariant refinable spaces give rise to trial spaces of any desired degree of accuracy satisfying the Lady?enskaja-Babu?ka-Brezzi condition for any spatial dimension. Moreover, in the time dependent case efficient preconditioners for the Schur complements of the discrete systems of equations can be based on corresponding stable multiscale decompositions. The results are illustrated by some concrete examples of adapted wavelets and corresponding numerical experiments.     

A nonlinear Galerkin method for the Navier-Stokes equations

Modern large scale computing allows the utilization of a very large number of variables/modes for spatial discretization. Therefore the computer tends to be saturated by computations on small wavelengths that carry a small percentage of the total energy. We advocate the utilization of algorithms treating differently small wavelengths and large wavelengths and we present here an algorithm of this sort, the nonlinear Galerkin method, stemming from the dynamical system theory.     

A local discontinuous Galerkin method for a doubly nonlinear diffusion equation arising in shallow water modeling

In this paper, we study a local discontinuous Galerkin (LDG) method to approximate solutions of a doubly nonlinear diffusion equation, known in the literature as the diffusive wave approximation of the shallow water equations (DSW). This equation arises in shallow water flow models when special assumptions are used to simplify the shallow water equations and contains as particular cases: the Porous Medium equation and the parabolic p-Laplacian. Continuous in time a priori error estimates are established between the approximate solutions obtained using the proposed LDG method and weak solutions to the DSW equation under physically consistent assumptions. The results of numerical experiments in 2D are presented to verify the numerical accuracy of the method, and to show the qualitative properties of water flow captured by the DSW equation, when used as a model to simulate an idealized dam break problem with vegetation.     

A procedure for the Galerkin method for a vibrating system

In this paper, we apply the Galerkin method to the problem of vibration of a one-dimensional system with free end conditions. Giving a MAPLE^®procedure, we test the results on two numerical examples.     

A discontinuous Galerkin method¶for the plate equation

We present a discontinuous Galerkin method for the plate problem. The method employs a discontinuous approximation space allowing nonmatching grids and different types of approximation spaces. Continuity is enforced weakly through the variational form. Discrete approximations of the normal and twisting moments and the transversal force, which satisfy the equilibrium condition on an element level, occur naturally in the method. We show optimal a priori error estimates in various norms and investigate locking phenomena when certain stabilization parameters tend to infinity. Finally, we relate the method to two classical elements: the nonconforming Morley element and the C ¹ Argyris element. Received: October 2000 / Accepted in revised form: December 2001     

同源性检测矩阵法的建立及应用*

矩阵理论是一门在各个领域运用广泛的学科,将其运用于同源性的检测。首先从氨基酸的同义密码子角度定义了一个反映两序列间同源性的公式,然后建立矩阵并在矩阵上定义运算来检测S的任一非空子集与T的任一非空子集的同源性,命名这种方法为矩阵法,在此基础上进行逐步搜索。通过选取GenBank中的具体序列进行数值实验,与MEGA软件的分析结果对比,证明了矩阵法在逐步搜索过程中的科学性和合理性。     

A lumped Galerkin method for solving the Burgers equation

A numerical solution of the one-dimensional Burgers equation is obtained using a lumped Galerkin method with quadratic B-spline finite elements. The scheme is implemented to solve a set of test problems with known exact solutions. Results are compared with published numerical and exact solutions. The proposed scheme performs well. A linear stability analysis shows the scheme to be unconditionally stable.     

A Runge-Kutta discontinuous Galerkin method for the Euler equations

This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for the Euler equations of gas dynamics from the viewpoint of kinetic theory. Like the traditional gas-kinetic schemes, our proposed RKDG method does not need to use the characteristic decomposition or the Riemann solver in computing the numerical flux at the surface of the finite elements. The integral term containing the non-linear flux can be computed exactly at the microscopic level. A limiting procedure is carefully designed to suppress numerical oscillations. It is demonstrated by the numerical experiments that the proposed RKDG methods give higher resolution in solving problems with smooth solutions. Moreover, shock and contact discontinuities can be well captured by using the proposed methods.     

不完备信息系统下的不确定性度量方法

在不完备信息系统中,不确定性度量是Rough Set理论中的一个难题。文中通过分析现有完备信息系统的不确定度量方法以及不完备信息系统的特性,提出了广义相似关系,并以之为基础给出了一个直接度量不完备信息系统不确定性的方法。通过实例分析,验证了该方法的有效性。     

复杂工业过程特征建模方法及应用研究

针对复杂工业过程的特征建模是研究其优化控制的基础.复杂工业过程普遍具有强干扰、非线性、大时变等诸多不确定性特征,部分工艺涉及复杂的生化反应并伴有强污染和高危性,检测数据具有维度高、噪声大等特性,这均为建立精准的工业模型提出了更急迫的需求和更高的标准.鉴于此,总结并归纳当前复杂工业过程的建模思路和研究进展,旨在从多个视角分析不同建模方法的适用性和有效性,为先进的优化控制理论指导实际工业生产奠定模型基础.首先,从机理建模、数据驱动建模和混合建模3个方向对目前主流的工业建模方法进行划分和综述;然后,阐述各类建模方法的具体设计思路,并分析模型结构和算法特点;接着,调研不同建模策略在解决实际工业过程中的指标建模、被控对象建模、全流程建模等问题的具体应用情况;最后,结合目前工业智能化建设趋势及其面临的挑战性问题,指出未来的研究思路和发展方向.     

A probabilistic wavelet system for stochastic and incomplete data-based modeling.

A probabilistic wavelet system (PWS) is proposed to model the unknown dynamic system with stochastic and incomplete data. When compared with the traditional wavelet system, the PWS uses a novel three-domain wavelet function to make a balance among the probability, time, and frequency domains, which achieves a robust modeling performance with poor data information. The definition, transformation, multiple-resolution analysis, and implementation of the PWS are presented to construct the whole theoretical framework. Simulation studies show that the performance of the proposed PWS is superior to the traditional one in a stochastic and incomplete data environment.     

Joint learning affinity matrix and representation matrix for robust low-rank multi-kernel clustering

Applied Intelligence - Multi-kernel subspace clustering has attracted widespread attention, because it can process nonlinear data effectively. It usually solves the representation coefficient...     

Conventional modeling of the multilayer perceptron using polynomialbasis functions

A technique for modeling the multilayer perceptron (MLP) neural network, in which input and hidden units are represented by polynomial basis functions (PBFs), is presented. The MLP output is expressed as a linear combination of the PBFs and can therefore be expressed as a polynomial function of its inputs. Thus, the MLP is isomorphic to conventional polynomial discriminant classifiers or Volterra filters. The modeling technique was successfully applied to several trained MLP networks.