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.     

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.     

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.     

遗传算法的收敛性统一判据

本文针对遗传算法的过早收敛或者收敛缓慢甚至不收敛,进行了详细的分析;理论分析了算法发生过早收敛的原因,收敛速度与各个控制参数和遗传操作的关系;提出并严格证明了与编码方式和选择策略无关的判断遗传算法收敛性判据。     

Uniformly Effective Numerical Methods for Hyperbolic Systems

A unified method to compute compressible and incompressible flows is presented. Accuracy and efficiency do not degrade as the Mach number tends to zero. A staggered scheme solved with a pressure correction method is used. The equation of state is arbitrary. A Riemann problem for the barotropic Euler equations with nonconvex equation of state is solved exactly and numericaly. A hydrodynamic flow with cavitation in which the Mach number varies between 10⁻³ and 20 is computed. Unified methods for compressible and incompressible flows are further discussed for the flow of a perfect gas. The staggered scheme with pressure correction is found to have Mach-uniform accuracy and efficiency, and for the fully compressible case the accuracy is comparable with that of established schemes for compressible flows. Received October 20, 1999; revised May 26, 2000     

运动矢量加速度预测起始搜索点的块匹配算法

块匹配运动估计是去除图像序列时间冗余的重要手段,在MPEG-4、H.264/AVC等视频编码标准中都得到了应用,但消耗了巨大的运算量.论文阐述了块匹配算法原理,归纳了当前运动估计中采用的各种手段,建议使用一种运动矢量加速度预测搜索起点的算法,利用相邻的若干参考帧中对应块的运动加速度来预测待编码块的起始运动矢量.仿真结果证明该方法效果明显,减少了搜索次数且准确度高.     

采用单片机实现的角加速度测量电路

文章提出了一种直接测量角加速度的单片机系统 ,详细介绍了系统硬件结构和程序框图 ,并分析了测量误差     

一种在高加速下测量位移和速度的方法

利用光纤传感器实现了可在高加速度下物体平动位移和速度的测试,实验证明了该方法的有效性,对产生误差的原因进行了分析.这是一种非接触的测试方法,可以测量加速度在200g以上时的位移和速度.