Numerical Methods for Hyperbolic Functional Differential Problems on the Haar Pyramid

The paper deals with the local Cauchy problem for nonlinear functional differential systems. We investigate a general class of difference methods for this problem. We construct interpolating operators on the Haar pyramid and we give an error estimate for approximate solutions. We adopt nonlinear estimates of the Perron type for given functions with respect to the functional variable. The proof of the stability is based on functional difference inequalities.     

A Priori Error Estimates for Optimal Control Problems Governed by Transient Advection-Diffusion Equations

In this paper, we investigate a characteristic finite element approximation of quadratic optimal control problems governed by linear advection-dominated diffusion equations, where the state and co-state variables are discretized by piecewise linear continuous functions and the control variable is approximated by piecewise constant functions. We derive some a priori error estimates for both the control and state approximations. It is proved that these approximations have convergence order , where h _U and h are the spatial mesh-sizes for the control and state discretization, respectively, and k is the time increment. Numerical experiments are presented, which verify the theoretical results. This research was supported by the National Basic Research Program of China (No. 2007CB814906) and the National Natural Science Foundation of China (No. 10771124).     

Solution Techniques for Constraint Satisfaction Problems: Foundations

The Constraint Satisfaction Problem (CSP) is ubiquitous in artificialintelligence. It has a wide applicability, ranging from machine visionand temporal reasoning to planning and logic programming. This paperattempts a systematic and coherent review of the foundations ofthe techniques for constraint satisfaction. It discusses in detail thefundamental principles and approaches. This includes an initialdefinition of the constraint satisfaction problem, a graphical meansof problem representation, conventional tree search solutiontechniques, and pre-processing algorithms which are designed to makesubsequent tree search significantly easier.     

《概率论与数理统计》教学中需要注意的几个问题

《概率论与数理统计》是一门研究随机现象统计规律的课程,是经济、管理、统计等各专业的必修课。通过多年的教学实践与反思,总结出教学中应该注意的两大问题,一是应该注重概念的讲解,二是在计算概率时应该反复强调分析事件的重要性,并且通过具体生动地案例来演示如何在讲课时做好上述两个方面的内容。     

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     

Kinetic Monte Carlo Method: Mathematical Foundations and Applications for Physics of Low-Dimensional Nanostructures

The kinetic Monte Carlo (kMC) method is an indispensable method for studying atomic and molecular systems, which makes it possible to solve a wide range of problems associated with atomic diffusion, the formation of defects and chemical compounds of various types, as well as the growth and self-organization of nanostructures. In this paper, we consider the fundamentals of the kMC and its modern modifications, both rigid-lattice and off-lattice. Particular attention is focused on constructing self-learning algorithms based on different methods for finding the saddle points of potential energy and on the techniques for the acceleration of the Monte Carlo method. Every considered method is illustrated by relevant examples mostly associated with the physics of metal surfaces.     

A Non-Overlapping Domain Decomposition Method for the Advection-Diffusion Problem

The application of a non-overlapping domain decomposition method to the solution of a stabilized finite element method for elliptic boundary value problems is considered. We derive an a-posteriori error estimate which bounds the error on the subdomains by the interface error of the subdomain solutions. As a by-product, some foundation is given to the design of the interface transmission condition. Numerical results support the theoretical results. Furthermore, we adapt a recent result on a-posteriori estimates for singular perturbation problems in order to obtain an a-posteriori estimate for the discrete subdomain solutions.     

Large-Dimensional Mathematical Programming Problems: A Solution Approach

An algorithm is designed for numerically solving large-dimensional mathematical programming problems, in which only the variables in linear constraints play a dominant role.     

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.     

弯管状屏蔽物体的数字仿形研究

为了预测核电站中弯管状屏蔽体的辐射衰减率,该文用数值解析法对弯管状屏蔽物体进行了仿形研究。在判断从放射线源到评价点的放射线是否穿透此弯管状屏蔽体时,提出了弯管状屏蔽体的假想外接长方体的建模方法,从而可避免建立弯管曲面方程的繁琐,将超越方程联立解的复杂计算简化为一次代数方程的简单计算,大幅度地缩短了计算时间。实际应用的结果验证了该方法的有效性。     

Galerkin Methods for Stochastic Hyperbolic Problems Using Bi-Orthogonal Polynomials

This work is concerned with scalar transport equations with random transport velocity. We first give some sufficient conditions that can guarantee the solution to be in appropriate random spaces. Then a Galerkin method using bi-orthogonal polynomials is proposed, which decouples the equation in the random spaces, yielding a sequence of uncoupled equations. Under the assumption that the random wave field has a structure of the truncated KL expansion, a principle on how to choose the orders of the approximated polynomial spaces is given based on the sensitivity analysis in the random spaces. By doing this, the total degree of freedom can be reduced significantly. Numerical experiments are carried out to illustrate the efficiency of the proposed method.     

Queueing Theory for Semiconductor Manufacturing Systems: A Survey and Open Problems

This paper surveys applications of queueing theory for semiconductor manufacturing systems (SMSs). Due to sophisticated tool specifications and process flows in semiconductor manufacturing, queueing models can be very complicated. Research efforts have been on the improvement of model assumptions and model input, mainly in the first moment (averages) and the second moment (variations). However, practices show that implementation of classical queueing theory in semiconductor industry has been unsatisfactory. In this paper, open problems on queueing modeling of SMS are discussed. A potential solution is also proposed by relaxing the independent assumptions in the classical queueing theory. Cycle time reduction has constantly been a key focus of semiconductor manufacturing. Compared with simulation, queueing theory-based analytical modeling is much faster in estimating manufacturing system performance and providing more insights for performance improvement. Therefore, queueing modeling attracts generous semiconductor research grants. Unfortunately, existing queueing models focus on simple extensions of the classical queueing theory and fail to question its applicability to the complicated SMS. Hence, related researches have not been employed widely in the semiconductor industry. In this paper, we conduct a survey on the important works and also present some open problems. We also propose a novel solution by relaxing a key assumption in the classical queueing theory. We are currently funded by Intel to explore this potential solution, and we hope it can foster an interesting research field for the years to come.     

催化裂化提升管反应器数学模拟新方法

催化裂化提升管反应器数学模型基本上都是基于平推流反应器的假设建立起来的,但是由于其内部流动、传热以及反应过程非常复杂、偏离平推流较大,所以在模型的实际应用中必须用装置因数去校正,表现出较强的经验性,为了改变这种状况,本文通过研究分析,提出了对催化裂化提升管反应器进行多维微分模拟的研究方法,从根本上把反应器结构尺寸、物流入口条件,流动特征及传热特征等影响考虑进来,把流动、传热、传质、裂化反应以及湍流脉动作用全部纲入模型中,建立催化裂化提升管反应器的流动反应综合模型,通过对模型的求解,可以得到提升管反应器内催化剂颗粒及油气的速度分布、温度分布以及组分分布,从而揭示工业提升管反应器内的化学工程信息。这些数据对工业提升管反应器的设计、操作优化及新技术的实施都是十分重要的。     

Minimal Stabilization for Discontinuous Galerkin Finite Element Methods for Hyperbolic Problems

We consider a discontinuous Galerkin finite element method for the advection–reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in the standard h-weighted graphnorm and obtain optimal order error estimates with respect to mesh-size. The second author was supported by the Swiss National Science Foundation.     

Higher Order Finite Volume Central Schemes for Multi-dimensional Hyperbolic Problems

Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order accurate finite volume central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and shock capturing nature of the scheme are demonstrated in various nonlinear multi-dimensional problems. In order to show the overall performance of the present central scheme numerical errors and non-oscillatory behavior are compared with existing multi-dimensional CWENO based central schemes for various multi-dimensional problems. Moreover, the benefits of the present fourth order central scheme over third order implementation are shown by comparing the numerical dissipation and computational cost between the two.