A Tailored Finite Point Method for a Singular Perturbation Problem on an Unbounded Domain

In this paper, we propose a tailored-finite-point method for a kind of singular perturbation problems in unbounded domains. First, we use the artificial boundary method (Han in Frontiers and Prospects of Contemporary Applied Mathematics, [2005]) to reduce the original problem to a problem on bounded computational domain. Then we propose a new approach to construct a discrete scheme for the reduced problem, where our finite point method has been tailored to some particular properties or solutions of the problem. From the numerical results, we find that our new methods can achieve very high accuracy with very coarse mesh even for very small ε. In the contrast, the traditional finite element method does not get satisfactory numerical results with the same mesh. Han was supported by the NSFC Project No. 10471073. Z. Huang was supported by the NSFC Projects No. 10301017, and 10676017, the National Basic Research Program of China under the grant 2005CB321701. R.B. Kellogg was supported by the Boole Centre for Research in Informatics at National University of Ireland, Cork and by Science Foundation Ireland under the Basic Research Grant Programme 2004 (Grants 04/BR/M0055, 04/BR/M0055s1).     

Tailored Finite Point Method for First Order Wave Equation

Following the idea of the tailored finite point method proposed in Han and Huang (J. Comput. Math. 26:728–739, 2008) and Huang (Netw. Heterog. Media 4:91–106, 2009), a series of efficient numerical schemes are developed for the one dimensional scalar wave equation within various types of media. Stability and accuracy are analyzed and numerically verified. In particular we can obtain unconditionally stable implicit schemes that can be solved explicitly for boundary value problems. We can also deal with the propagation of discontinuity and highly oscillatory waves efficiently. The generalization to higher order schemes is straightforward.     

高阶系统的奇异摄动模型的平衡降阶

随着控制理论和电子计算机技术的迅速发展,尽管为研究与设计高阶复杂系统提供了方便的条件,但是对复杂高阶系统进行模型简化仍然是控制系统设计与仿真工作者的一个重要研究课题.针对奇异摄动模型的平衡降阶方法,提出了采用时矩输出拟合来改善降阶系统输出响应逼近程度的改进方法,通过给出的实例仿真证实了这一点.     

On the Convergence of a Spline Method for Singular Two Point Boundary Value Problems Arising in Physiology

The second order spline method developed by Iyengar et al. [11] for the problems $$eqalign{ x^{-alpha}(x^alpha y^prime)^prime & = f(x,y),quad 0     

Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients

Finite difference operators approximating second derivatives with variable coefficients and satisfying a summation-by-parts rule have been derived for the second-, fourth- and sixth-order case by using the symbolic mathematics software Maple. The operators are based on the same norms as the corresponding approximations of the first derivative, which makes the construction of stable approximations to general multi-dimensional hyperbolic-parabolic problems straightforward.     

Application of the Over-Set Grid Technique to a Model Singular Perturbation Problem

The numerical solution of a singularly perturbed problem, in the form of a two-dimensional convection-diffusion equation, is studied by using the technique of over-set grids. For this purpose the Overture software library is used. The selection of component grids is made on basis of asymptotic analysis. The behavior of the solution is studied for a range of small diffusion parameters. Also the possibilities of rotating the grid with the convection direction is considered. The basic discretisation method is central differencing, and in order to fit global properties of the solution, the composite grid used is made parameter dependent. In view of possible ɛ-uniform convergence, in the resulting composite grid the number of grid points is kept constant for the different values of the small parameter. Only the grid spacing is adapted, depending on the parameters. We see that, even with such careful adaptation of the grid, in the discrete maximum norm no ɛ-uniform convergence is achieved. Received October 10, 1999     

Application of an Adaptive Sparse-Grid Technique to a Model Singular Perturbation Problem

In this paper we show how, under minimal conditions, a combination extrapolation can be introduced for an adaptive sparse grid. We apply this technique for the solution of a two-dimensional model singular perturbation problem, defined on the domain exterior of a circle. Received October 18, 1999     

指纹图像奇异点提取的一种鲁棒方法

提出了一种改进的奇异点的提取方法,选通过改进的Poincare指数计算,挑选出符合条件的候选点,然后在此基础上,利用径向方向会聚性,前景,背景分割和概率分布来筛选修选奇异点,用该方法对不同质量的指纹图像进行实验,并与经典方法进行比较,结果表明该方法更加有效、可靠,也具有更好的鲁棒性。     

Jacobi Neural Network Method for Solving Linear Differential-Algebraic Equations with Variable Coefficients

Neural Processing Letters - A novel Jacobi neural network method is proposed for solving linear differential-algebraic equations (DAEs) in the paper. First, Jacobi neural network is applied to...     

一类奇异非线性变结构控制系统的跟踪问题

首次利用变结构控制方法研究了一类奇异非线性系统的模型跟踪问题，在不同情况下，通过引入动态补偿器的概念，设计了奇异模型跟踪系统的切换函数，得到了在切换面上实现跟踪的条件，然后利用趋近律方法设计了变结构控制，以保证在切换面外的运动在有限时间到达切换面，通过滑动运动实现跟踪，最后讨论了参数模型为正常系统的线性定常奇异系统的跟踪问题。     

The Highest Superconvergence Analysis of ADG Method for Two Point Boundary Values Problem

In this paper, an averaging discontinuous Galerkin (ADG) method for two point boundary value problems is analyzed. We prove, for any even polynomial degree k, the numerical flux convergence at a rate of \(2k+2\) for all mesh nodes (in particular, the numerical flux for \(k=0\) has the second order superconvergence rate). Numerical experiments are shown to demonstrate the theoretical results.     

A Mixed Finite Element Method for Elasticity in Three Dimensions

We describe a stable mixed finite element method for linear elasticity in three dimensions.     

A Singular Value Decomposition-Based Method for Solving a Deterministic Adaptive Problem

A computational scheme based on the singular value decomposition (SVD) for a deterministic, data domain approach to the adaptive processing problem is presented. In the direct data domain approach, a single snapshot is considered for an assumed direction of arrival with unknown amplitude. This unknown signal strength is estimated on a snapshot by snapshot basis. The new SVD based method is compared with the QZ method for determining the generalized eigenvalues of a system. Their performance in estimating the strength of signals of interest in the presence of main beam jammers, clutter, and thermal noise is considered. Limited examples have been presented to illustrate the two methods.     

A Nonrecursive Solution Method for the Linear-Quadratic Optimal Control Problem with a Singular Transition Matrix

In the optimal linear regulator problem the control vector is usually determined by solving the algebraic matrix Riccati equation using successive substitutions. This, however, can be rather inefficient from a computational point of view. A nonrecursive method which requires that the transition matrix is nonsingular has been proposed by Vaughan (1970). In the present paper we present a nonrecursive solution to the matrix Riccati equation for the case that the transition matrix may be singular. We show that this procedure leads to the same numerical results as the standard iteration of the matrix Riccati equation.     

The Singular Sources Method for an Inverse Transmission Problem

We employ the singular sources method introduced in [4] to solve an inverse transmission scattering problem for the Helmholtz equation or D, respectively, where the total field u satisfies the transmission conditions on the boundary of some domain D with some constant β. The main idea of the singular sources scheme is to reconstruct the scattered field of point sources or higher multipoles (·, z) with source point z in its source point from the far field pattern of scattered plane waves. The function (z, z) is shown to become singular for z→∂D. This can be used to detect the shape D of the scattering object.Here, we will show how in addition to reconstructions of the shape D of the scattering object, the constant β can be reconstructed without solving the direct scattering problem. This extends the singular sources method from the reconstruction of geometric properties of an object to the reconstruction of physical quantities.     

Output Feedback Stabilization for an ODE Coupled with a Wave Equation with Variable Coefficients

International Journal of Control, Automation and Systems - In this paper, we are concerned with the output feedback problem for coupled ODE-wave systems subject to spatially-varying coefficients....     

小型风电系统变步长扰动MPPT控制仿真研究

最大功率跟踪(MPPT)策略是提高风电系统功率转换效率的重要方法.文中提出了变步长扰动MPPT策略,并在MATLAB仿真环境中,开发了带有此策略的小型风电系统仿真模型.该模型包括风力机模型、永磁发电机(PMSG)模型、DC/DC斩波器模型、负载功率采样模型和MPPT控制模型等.利用该模型进行计算机仿真,给出了一定风速下负载功率和发电机输出功率的仿真结果.结果表明:实现了变步长扰动MPPT策略控制的仿真,与传统固定步长MPPT策略相比,提高了最大功率跟踪的快速性和准确性,进而提高了风能转换效率.