Convergence acceleration for the steady-state Euler equations

We consider the iterative solution of systems of equations arising from discretizations of the non-linear Euler equations governing compressible flow. The differential equation is discretized on a structured grid, and the steady-state solution is computed by a time-marching method.A convergence acceleration technique based on semicirculant approximations of the difference operator or the Jacobian is used. Implementation issues and variants of the scheme allowing for a reduction of the arithmetic complexity and memory requirement are discussed. The technique can be combined with a variety of iterative solvers, but we focus on non-linear explicit Runge-Kutta time-integration schemes. The results show that the single-stage forward Euler method can be used, and that the time step is not limited by a CFL-criterion. This results in that the arithmetic work required for computing the solution is equivalent to the work required for a fixed number of residual evaluations.     

Discrete Fundamental Solution Preconditioning for Hyperbolic Systems of PDE

We present a new preconditioner for the iterative solution of systems of equations arising from discretizations of systems of first order partial differential equations (PDEs) on structured grids. Such systems occur in many important applications, including compressible fluid flow and electromagnetic wave propagation. The preconditioner is a truncated convolution operator, with a kernel that is a fundamental solution of a difference operator closely related to the original discretization. Analysis of a relevant scalar model problem in two spatial dimensions shows that grid independent convergence is obtained using a simple one-stage iterative method. As an example of a more involved problem, we consider the steady state solution of the non-linear Euler equations in a two-dimensional, non-axisymmetric duct. We present results from numerical experiments, verifying that the preconditioning technique again achieves grid independent convergence, both for an upwind discretization and for a centered second order discretization with fourth order artificial viscosity.     

Discrete Supervisory Control of Hybrid Systems Based on l-Complete Approximations

The topic of this paper is the synthesis of discrete supervisory control for hybrid systems with discrete external signals. Such systems are in general neither l-complete nor can they be represented by finite state machines. Our solution to the control problem is as follows: we find the strongest l-complete approximation (abstraction) _l for , represent it by a finite state machine, and investigate the control problem for the approximation. If a solution exists on the approximation level, we synthesize the maximally permissive supervisor for _l . We show that it also solves the control problem for the underlying hybrid system . If no solution exists, approximation accuracy can be increased by computing the strongest k-complete abstraction _k , k > l. The basic ideas regarding the approximation step are explained within the framework of Willems' behavioral systems theory. Implementation issues are treated in a state space framework, and the main results are interpreted from a traditional control engineering point of view.     

方程迭代求根加速收敛的算法研究

本文介绍了方程迭代求根的方法．以迭代法的收敛性和收敛速度为出发点，提出并讨论了采用迭代值的组合和方程式的变换等技巧来提高迭代的收敛性并加快其收敛速度的算法．文中对算法进行了描述，并用具体实例证明了该算法的有效性．     

Formulations for Numerically Approximating Hyperbolic Systems Governing Sediment Transport

This paper investigates the accurate numerical solution of the equations governing bed-load sediment transport. Two approaches: a steady and an unsteady approach are discussed and five different formulations within these frameworks are derived. A flux-limited version of Roe's scheme is used with the different formulations on a channel test problem and the results compared.     

Method of Successive Approximations for Solving Integral Equations of the Theory of Risk Processes

A model of a classical risk process describing the evolution of an insurance company's capital is generalized. Integral equations for the bankruptcy probability are derived. The method of successive approximations is used to solve these equations.     

Convergence acceleration for computing steady-state compressible flow at low Mach numbers

A novel technique is introduced to accelerate the convergence of compressible low Mach number flow computations to the steady state. The stiffness due to the large disparity of flow velocity and acoustic wave speeds is bypassed by artificially reducing the speed of sound and thereby increasing the Mach number. This Mach number transformation is achieved by subtracting a constant value from the pressure in the entire flow field. Only the inviscid terms of the energy equation are influenced by that pressure decrease. The steady-state error is corrected by solving a scalar equation after each time step such that the steady-state solutions of the modified and non-modified schemes coincide. Thus, for each low Mach number simulation, one can obtain a convergence performance comparable to the corresponding simulation with a Mach number of about 0.4. This convergence acceleration is demonstrated for premixed laminar flames. If the present technique is implemented without time splitting, it corresponds to a novel low Mach number preconditioning.     

On some approaches to solve CFD problems

This paper presents two efficient methods for spatial flows calculations. In order to simulate of incompressible viscous flows, a second-order accurate scheme with an incomplete LU decomposed implicit operator is developed. The scheme is based on the method of artificial compressibility and Roe flux-difference splitting technique for the convective terms. The numerical algorithm can be used to compute both steady-state and time-dependent flow problems. The second method is developed for modeling of stationary compressible inviscid flows. This numerical algorithm is based on a simple flux-difference splitting into physical processes method and combines a multi level grid technology with a convergence acceleration procedure for internal iterations. The capabilities of the methods are illustrated by computations of steady-state flow in a rotary pump, unsteady flow over a circular cylinder and stationary subsonic flow over an ellipsoid.     

Convergence of the spline function for functional-differential equation of neutral type

The existence, uniqueness and stability for the functional-differential equation of neutral type using spline of deficiency 3 with stepsize 3h spline function of degree four are presented in Ref. [1]. In this paper, we extend the study to the convergence of our proposed spline method. We prove that, if the local error is of order p, then the global error is of order p as well. Numerical examples are presented to illustrate the convergence of the method.     

并行模糊系统的预测和辨识收敛性

自1965年L.A.Zadeh提出模糊集理论以来,模糊理论已经在非线性系统辨识、函数逼近、模式识别、机器学习等领域得到了极广泛的应用。由于人的推理在本质上是模糊的,因此使用模糊理论处理实际问题时更符合人的处理过程,这就极大地提高了人类解决问题的能力。在模糊理论的应用当中,非线性系统辨识是最重要的方向之一。一般说来,模糊系统可以以两种方式用于非线性系统辨识:串并行方式和并行方式(见图1,图2)。其中TDL表示时间延迟逻辑,RS表示待辨识的实际系统,FS表示模糊系统。图1称为串并行方式,图2称为并行方式。在大部分实际应用当中使用的是串并行方式,     

基于像素光照计算的硬件加速技术

给出了基于像素光照计算的原理和硬件体系结构;提出了一种基于像素光照计算的设计分析方法及相应的光照计算参数的纹理表示模型;通过凹凸纹理的实时绘制,给出了不同硬件加速模式下的实现结果.     

Convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations

This paper deals with the convergence and stability of the semi-implicit Euler method for linear stochastic delay integro-differential equations. It is proved that the semi-implicit Euler method is convergent with strong order p=0.5. The condition under which the method is asymptotic mean square stable is determined and numerical experiments are presented.     

Relaxation Schemes for Hyperbolic Conservation Laws with Stiff Source Terms: Application to Reacting Euler Equations

We deal in this paper with the numerical study of relaxation schemes for hyperbolic conservation laws including stiff source terms. Following Jin and Xin [11], we use semi-linear hyperbolic systems with a stiff source term to approximate systems of conservation laws. This method allows to avoid the use of a Riemann solver in the construction of the numerical schemes. Numerical tests are presented together with an application to Reactive Euler Equations.     

柔性机械手加速度反馈消振的进一步研究

在柔性机械手的控制中,加速度反馈的方法是一种消除末端振动的有效而简便途径。然而,目前对其有效性尚无严格的理论证明和分析。本文将通过非约束模态分析方法对单柔性臂机械手的动力学方程进行了分析,以此为基础对加速度反馈的理论和实现进行了研究和讨论,得到了一些重要的结论。     

Nonminimal Kane's Equations of Motion for Multibody Dynamical Systems Subject to Nonlinear Nonholonomic Constraints

Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations. Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint equations for a holonomically constrained particle in the gravitational field.     

Convergence of gradient-based iterative solution of coupled Markovian jump Lyapunov equations

The solution of coupled discrete-time Markovian jump Lyapunov matrix equations (CDMJLMEs) is important in stability analysis and controller design for Markovian jump linear systems. This paper presents a simple and effective iterative method to produce numerical solutions to this class of matrix equations. The gradient-based algorithm is developed from an optimization point of view. A necessary and sufficient condition guaranteeing the convergence of the algorithm is established. This condition shows that the algorithm always converges provided the CDMJLMEs have unique solutions which is evidently different from the existing results that converge conditionally. A simple sufficient condition which is easy to test is also provided. The optimal step size in the algorithm such that the convergence rate of the algorithm is maximized is given explicitly. It turns out that an upper bound of the convergence rate is bounded by a function of the condition number of the augmented coefficient matrix of the CDMJLMEs. Some parameters are introduced to the algorithm that will potentially reduce the condition number and thus increase the convergence rate of the algorithm. A numerical example is used to illustrate the efficiency of the proposed approach.     

Arduino开源平台在低成本加速度与动态位移直接测量中的应用

实时位移是结构健康监测及振动控制所需的重要参数,但固定参考点式位移计法及非接触摄录式位移测量法成本均较高,而加速度二次积分重构位移算法受积分初始条件影响导致误差可控性差。本研究利用Arduino开源微控制器平台的开放性和微电子机械系统(Micro-Electro-Mechanical-Systems,MEMS)型加速度计的成本优势,结合内嵌式加速度重构位移Lee算法对积分初值条件的低依赖性特征,开发了一种低成本、加速度和动态位移直接测量系统,并配合内置SD卡模块实现了实时采样、数据存储功能。基于小型振动台对比实验,验证了该系统对简谐振动、地震动加速度、桥梁墩顶横向位移测量的有效性和精度。结果表明:地震动加速度激振下,该系统与成熟加速度测量系统峰值误差低于7%;实测桥梁墩顶横向位移激振下,该系统与线性可变差动变压器式相对位移计(Linear-Variable-Differential-Transformer,LVDT)最大测量误差低于10%。     

用EMD和小波消噪的加速度信号压缩重构新方法

针对噪声破坏加速度信号稀疏性、降低其压缩感知重构算法性能问题,提出了一种用经验模态分解(EMD)和小波分析联合消噪的加速度信号压缩重构新方法.该方法首先采用EMD和小波阈值联合消噪方法对加速度信号消噪处理,保持加速度信号内在稀疏性;然后基于压缩感知理论和加速度信号块结构信息,采用块稀疏贝叶斯学习算法以高概率重构原始加速度信号.采用USC-HAD人体日常行为数据库中的加速度信号验证本文方法的有效性.实验结果表明,本文所提方法的信噪比和均方根误差明显优于未经消噪处理的压缩感知重构算法,能够有效抑制加速度信号噪声,增大加速度信号稀疏度,提高加速度信号压缩重构算法性能.     

对象集变化时近似集动态维护的矩阵方法

目前粗糙集模型中概念的上、下近似集的计算方法大多是基于静态信息系统的.而实际的信息系统是随时间动态变化的,通常包括对象集、属性集和属性值3种类型的粒度变化,这些变化必然引起概念近似集的动态变化.如何快速、有效地更新概念的近似集是基于粗糙集的动态知识更新中的热点研究问题之一.而利用既有知识的增量式更新方法是一种有效的近似集动态更新方法.在信息系统动态变化的客观环境下,以矩阵作为表达和运算工具从一个全新的视角研究信息系统的论域随时间变化时,变精度粗糙集模型中概念的上、下近似集的增量式更新方法,并构造出近似集增量式更新的矩阵算法,随后分析了算法的时间复杂度。进一步,在MATLAB平台上开发出增量式更新和非增量式更新近似集的两种矩阵算法的程序,最后在UCI的6个数据集上测试了两种矩阵算法的性能并将实验结果进行比较,结果表明增量式更新的矩阵算法可行、简洁和高效.