A two-grid method applied to plane elasticity

A coarse-grid correction method has been applied to solve the linear system obtained by the finite element approximation of linear elasticity in plane deformation. Different smoothers were used and rates of convergence were computed and compared. The influence of the geometry was observed. This method was shown to be very efficient for a rather large range of values of the rheological constant.     

On the multi-grid method applied to difference equations

Multi-grid methods are characterized by the simultaneous use of additional auxiliary grids corresponding to coarser step widths. Contrary to usual iterative methods the speed of convergence is very fast and does not tend to one if the step size approaches zero. The computational amount of one iteration is proportional toN, the number of grid points. Thus, a solution with accuracy ? requires 0 (|log ?|N) operations. In this paper we apply a multi-grid method to Helmholtz's equation (Dirichlet boundary data) in a general region and to a differential equation with variable coefficients subject to arbitrary boundary conditions.     

Spherical harmonics method applied to the multi-dimensional radiation transfer

The spectral radiation transfer equation in 2D axisymmetrical and 3D geometries is solved by the P₁-approximation of the spherical harmonics and ray-tracing methods. Martian atmosphere and typical entry conditions are considered. Navier–Stokes equations coupled with the nonequilibrium vibrational excitation and finite rate chemistry describe thermodynamically and chemically nonequilibrium gas. The multi-group model is used to model optical properties of CO₂–N₂ mixture. The developed methodology of integration of the P₁-approximation on unstructured grids and subsequent numerical solution allow us to reach reasonable agreement with the accurate ray-tracing method and drastically reduce the cost of solution of the radiation transfer equation in multi-dimensional geometries.     

Pulse-clamp method applied to SIROF stimulation electrodes

Miniaturized electrodes, structures, and devices are necessary to achieve high target selectivity during stimulation in single neuron networks, while significant charge transfer is essential. A reliable test method is required to evaluate charge injection capability for neural stimulation applications that demand both a large amount of charge injection and a small electrode size. A custom made pulse-clamp circuit was employed to characterize sputtered iridium oxide film (SIROF) microelectrodes. Pulse-clamp measurements with 400 μs long pulses are performed in 154 mM phosphate buffered saline (PBS) solution on planar microelectrodes smaller than 100 μm in diameter. A cell model was used to verify the circuit design with SPICE simulations. The pulse-clamp results of SIROF electrodes of different sizes show charge losses of less than 6%, even at high charge density levels.     

The decomposition method applied to stiff systems

The decomposition method is applied to a stiff system of differential equations to obtain a converging series which is summed for an analytic solution. Advantages over fourth- and fifth- order Runge-Kutta methods are shown.     

神经网络方法应用于轮廓定位

关于从图像中定位物体轮廓的问题,目前所采用的活动轮廓模型和基于自组织神经网络的算法,存在能量泛函优化容易陷入局部极值和演化过程依赖于初始轮廓的选取等问题。提出了一种基于RBF神经网络的轮廓定位算法。首先,通过自适应梯度阈值方法来获取图像特征点。然后,通过特征点的聚类建立一组基函数,把图像像素点的像素值和梯度构造输入向量空间,在网络权值训练完成后,利用网络的预测功能来准确判断物体轮廓。与传统算法相比,仿真结果表明提出的轮廓定位算法可以高效地实现目标轮廓定位。     

一种基于多分形奇异谱的噪声奇异性分析新方法

在介绍了噪声中的奇异性以及其全局奇异性的表征方法——多分形奇异谱的基础上,提出并实现了一种基于子波分解模极大的计算噪声多分形奇异谱的方法,通过对仿真信号验证,证明了该方法准确可靠。在对实测信号分析中,也发现该方法得到的多分形奇异谱比功率谱更能充分刻画噪声信号的特性。     

信号奇异性计算方法在电噪声信号中的应用*

为了快速准确地计算电噪声奇异性,在介绍信号奇异性计算方法的基础上,将其引入到电噪声信号分析中,提出一种新的基于多重分形奇异性指数计算信号电噪声的方法。新方法利用多重分形来提取电噪声中可以表达信号内在细节特征的奇异点Hlder指数,通过计算电噪声中Hlder指数的差异来进行噪声分析。通过对实测电迁移和光耦电噪声的计算分析表明,电迁移后期奇异性指数会发生突变;而良品光耦器件和次品光耦器件在信号噪声的平均Hlder指数方面差异明显。实验结果证明本方法是一种快速可靠的电噪声奇异性计算方法。     

The method of Ritz applied to the equation of Hamilton

Without any reference to the theory of differential equations, the initial value problem of the nonlinear, nonconservative double pendulum system is solved by the application of the method of Ritz to the equation of Hamilton. Also shown is an example of the reduction of the traditional eigenvalue problem of linear, homogeneous, differential equations of motion to the solution of a set of nonhomogeneous algebraic equations. No theory of differential equations is used. Solution of the time-space path of the linear oscillator is demonstrated and compared to the exact solution.     

Boundary element method applied to the analysis of thin plates

The classic Kirchhoff plate theory is formulated through integral representation decomposing the biharmonic field equation in two coupled harmonic equations. Two domain integrals appear, one inherent to the problem and the other due to the previous decomposition. Both of them are evaluated defining equivalent boundary integrations, using collocation method in several points on the boundary and the domain. These equivalent integrations are the same as those involved in the integral representation of the Poisson equation, therefore no extra integrations are needed.     

A cad method applied to the development of microwave oscillators

In this article, a method is proposed that allows the prediction of characteristic parameters of integrated microwave oscillators, i.e., operating frequency and distribution of the output power due to harmonic frequencies. This method combines rigorous field theoretical analysis of the linear environment with the “harmonic balance” approach. Relations between these areas are shown and discussed by means of numerical and experimental results. © 1994 John Wiley & Sons, Inc.     

A note on the accuracy of spectral method applied to nonlinear conservation laws

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear PDE with discontinuous solutions, Fourier spectral method will produce poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We have found out that the moments against analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a Gegenbauer polynomial based post-processing.Research supported by ARO Grant DAAL03-91-G-0123 and DAAH04-94-G-0205, NSF Grant DMS-9211820, NASA Grant NAG1-1145 and contract NAS1-19480 while the first author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23681-0001, and AFOSR Grant 93-0090.     

The complex method applied to optimal truss configuration

The Complex Method of Box is applied to the determination of optimal member sizes and geometric configuration for minimum weight of 3-dimensional truss structures. Design constraints include bounds on member size, joint coordinates, member stresses, Euler buckling and joint displacements. The displacement method of structural analysis is used and the system is assumed to be linearly elastic. Statically indeterminate structures under multiple loading conditions can be optimized and the sizing as well as the geometric design variables may be linked. Limited topological changes are permitted for designs which have small member forces.The design spaces for sizing and geometric variables are separated. Geometry is modified by the Complex Method and member sizes by stress ratio and a scaling procedure for stiffness.The method is applied to two numerical examples from the literature. Results indicate favourable design improvements and rates of convergence. Substantial additional improvement resulting from member deletion is demonstrated.     

Static load balancing applied to Schur complement method

A finite element method often leads to large sparse symmetric and positive definite systems of linear equations. We consider parallel solvers based on the Schur complement method on homogeneous parallel machines with distributed memory. A finite element mesh is partitioned by graph partitioning. Such partitioning results in submeshes with similar numbers of elements and, consequently, submatrices of similar sizes. The submatrices are partially factorised. The time spent on the partial factorisation can be different, i.e., disbalanced, because methods exploiting the sparsity of submatrices are used. This paper proposes a Quality Balancing heuristic that modifies classic mesh partitioning so that the partial factorisation times are balanced, which saves overall computation time, especially for time dependent mechanical and nonstationary transport problems.     

适用于遮挡车辆检测的子块带权模板匹配方法

针对多车辆跟踪过程中的遮挡问题,提出一种基于梯度方向直方图的子块带权模板匹配方法。该方法先对目标分块,并提取每块的梯度方向直方图,然后利用核函数为各块赋予不同权值,并采用子块带权特征匹配度度量方法计算目标模型与搜索窗的匹配度,进而获取最佳匹配。最后将该方法应用于多车辆跟踪过程中的遮挡车辆跟踪与检测。实验表明,该方法具有良好的精确度和鲁棒性。     

基于多元混合高斯分布的多分类人脸识别方法

针对实际人脸图像含有的噪声模型常常表现出的非高斯特性, 该非高斯特性具有较厚重的拖尾现象, 提出一种基于多元混合高斯分布的多分类人脸识别方法。该方法将多元混合高斯分布、核函数、概率密度函数估计中的参数估计以及贝叶斯理论结合起来, 能对含有重尾噪声的人脸图像有较高的识别率。用ORL标准人脸库进行验证, 实验结果表明了可行性。     

Augmented Lagrangian method applied to American option pricing

The American option pricing problem is originally formulated as a stochastic optimal stopping time problem. It is also equivalent to a variational inequality problem or a complementarity problem involving the Black-Scholes partial differential operator. In this paper, the corresponding variational inequality problem is discretized by using a fitted finite volume method. Based on the discretized form, an algorithm is developed by applying augmented Lagrangian method (ALM) to the valuation of the American option. Convergence properties of ALM are considered. By empirical numerical experiments, we conclude that ALM is more effective than penalty method and Lagrangian method, and comparable with the projected successive overrelaxation method (PSOR). Furthermore, numerical results show that ALM is more robust in terms of computation time under changes in market parameters: interest rate and volatility.     

Ns-kriging based microstructural optimization applied to minimizing stochastic variation of homogenized elasticity of fiber reinforced composites

This paper describes an approximate microstructural optimization using the ns-kriging (noise-resistant smoothed kriging) method for minimizing the maximum stochastic variation of homogenized elastic properties of a composite material caused by microscopic uncertainties of component materials. Since evaluation of a stochastic characteristic of a homogenized material property such as expectation or variance will involve a high computational cost and its results include inaccuracy in using the Monte Carlo simulation, an approximation-based optimization technique is useful for solving the optimization problem considering the multiscale stochastic problem. Especially, the ns-kriging will work well in case of using inaccurate data for an unknown objective function. In order to investigate applicability and effectiveness of the proposed ns-kriging based approach to the optimization problem, it is applied to the cross-sectional shape optimization of fiber in a unidirectional FRP. From the numerical results, validity and effectiveness of the proposed approach are confirmed.     

一种基于多级分割的指纹奇异点检测新方法

针对指纹图像奇异点检测中奇异点精确定位和可靠判断的难题,提出了一种基于多级分块尺寸的指纹奇异点检测新方法。首先,对于一枚指纹图像,在不同的分块尺寸下分别采用平滑和不平滑的方法进行指纹方向场的估计。然后,根据估计的指纹方向场信息进行指纹奇异点检测。接着,利用不同情况下检测的指纹奇异点位置相互关联的特性,进行指纹奇异点的精确定位、可靠判断。最后,在具有2500枚指纹的NJU 2000指纹数据库上的实验结果验证了该方法的有效性。