奇异延迟微分方程数值仿真的两步连续Runge-Kutta方法

提出在当前的积分步内计算级值时，放松延迟对计算的影响的思想，构造了一类奇异延迟微分方程数值仿真的两步连续Runge-Kutta方法(TSCRK)，讨论了方法的构造，方法阶条件，证明了方法的收敛性，分析了方法的稳定性。这类方法具有优良的稳定性和较高的阶级，并保持了显式的求解过程。数值试验表明方法是有效的。     

刚性延迟微分方程数值仿真的两步连续Rosenbrock方法

在科学、工程领域的研究和应用中,常常会遇到刚性延迟微分方程系统,对它们进行数值仿真时,通常需要稳定性较好计算复杂性小的方法。为了数值仿真刚性延迟微分方程系统,构造了一类用于求解刚性延迟微分方程的两步连续Rosenbrock方法,讨论了方法的构造,方法的阶条件,证明了方法的收敛性,分析了方法的稳定性。这种方法具有GP-稳定性,数值试验表明方法是有效的。     

爆炸冲击效应数值仿真中的几项关键技术

爆炸冲击效应的数值仿真，涉及到大变形、高应变率以及材料的破坏，传统的拉格朗日或欧拉方法在解决该问题均有很大的局限性，为克服或消除这些局限性，先后发展了网格重分、ALE、CEL、FLM、SPH等方法，各有所长，但尚未完全解决；而在实际工程中，切合实际的岩土介质本构关系则是数值仿真的关键；高效并行计算与可视化则是数值仿真的必由之路。     

一类组合两步连续RK-Rosenbrock方法

对于一个大的刚性延迟微分方程系统,除了延迟分量给予系统影响外,还常常会出现系统的解分量有的变化很快,而有的变化很慢的情况。此时,可以把大的刚性延迟微分方程系统分解成为两个耦合的子系统,一个是描述系统快变部分的刚性延迟子系统,另一个是描述系统慢变部分的非刚性延迟子系统。对于分解的刚性延迟微分方程大系统,构造了一类用于求解刚性延迟微分方程的组合两步连续RK-Rosenbrock方法,讨论了方法的构造,方法的阶条件,证明了方法的收敛性,分析了方法的稳定性,数值试验表明方法是有效的。     

An Improved Nonlinear Multistage Switch System of Microbial Fermentation Process in Fed-Batch Culture

This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.     

A Continuous Minimization Method for Solving Optimal Control Problem

ＡＣｏｎｔｉｎｕｏｕｓＭｉｎｉｍｉｚａｔｉｏｎＭｅｔｈｏｄｆｏｒＳｏｌｖｉｎｇＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍＡＣｏｎｔｉｎｕｏｕｓＭｉｎｉｍｉｚａｔｉｏｎＭｅｔｈｏｄｆｏｒＳｏｌｖｉｎｇＯｐｔｉｍａｌＣｏｎｔｒｏｌＰｒｏｂｌｅｍ￥ＧＵＲｏ...     

定性定量集成模型的求解技术研究

已有的模型求解技术较好地解决了连续模型、离散模型和连续离散混合模型等定量模型的求解问题,但是针对包含定性定量混合模型的求解问题尚缺乏很好的求解策略,大都仅针对于特定的定性模型与定量模型进行集成求解。引入定性定量集成模型求解技术将更好的解决这一问题。首先介绍了定性定量集成求解的相关工作,提出了定性定量集成模型的联合求解策略,包括时间管理与数据交互的方法及基于SRML的定性定量交互接口方法。最后,给出一个应用示例和结论。     

基于多粒度模型的导弹MDO方法研究

根据MDO环境的建模/仿真需求,针对某导弹多学科设计优化问题,分析了多粒度模型建模/仿真的必要性,以气动学科为例探讨了导弹MDO环境中多粒度模型的建模/仿真方法,研究了有限元分析软件FLUENT及其前处理软件GAMBIT的集成方法,并利用响应面分析、工程估算、数值计算三种方法对某导弹的气动学科进行多粒度的建模与解算,将输出的主要气动参数与风洞试验数据进行了比较与分析。研究结果表明多粒度模型的建模/仿真对提高导弹MDO效率具有重要意义。

Abstract：

According to the requirement of modeling and simulation in MDO environment, with consideration of missile’s Multidisciplinary Design Optimization problem, the necessity of modeling and simulation on multi-granularity model was analyzed. Taking pneumatic domain as an example, method of modeling and simulation on multi-granularity in missile’s MDO environment was discussed. The integration methods of finite element software FLUENT and its pre-processing software GAMBIT were studied. Through abundant experiments, data results of computing multi-granularity model were given using three methods, namely Response Surface Analysis, engineering prediction method and numerical computation method. Finally, comparison of the data got from above and from wind tunnel test was analyzed. The study results show that modeling and simulation on multi-granularity model are significant to improve MDO efficiency.     

Libor市场模型的Monte Carlo控制变量加速方法及并行实现

为了加速定价利率衍生产品的Monte Carlo模拟,对远期测度下Libor市场模型中的漂移项用确定性函数近似,构造了一个与原问题高度相关的控制变量. 然后将此控制变量算法移植到多核CPU和GPU的并行计算环境中,极大地提高了计算效率. 针对利率上限的数值结果表明选取的控制变量十分有效且稳健,多核CPU具有线性加速效果,GPU相对于单核CPU具有很大的计算优势,控制变量和并行计算结合得到的加速效果大致是两者的乘积. 结合控制变量和并行计算的方法可以为其他利率衍生产品如利率下限,互换期权的定价提供有效思路.     

基于聚合算法的失效相关多部件系统维修策略优化

针对多部件系统维修策略优化问题,在考虑失效相关和经济相关的基础上,从建模和求解算法两方面展开了研究。建立了多部件系统折扣准则模型,得到了维修费率的最优方程,并转化为线性规划问题。采用聚合算法减小线性规划问题的规模,并利用迭代算法求得其最优解。最后通过数值算例,说明了失效相关程度对折扣总成本以及最优维修策略的影响,探究了模型中成本参数对维修策略的影响。算法对比的实验结果显示,采用聚合迭代算法可以有效提高运算速度,降低内存占用。     

Innovations twostage dual control

1 .INTRODUCTIONWeconsiderthequadraticoptimalcontrolofalinearsystemwithunknownparameters .Thepresentcon trolsignalaffectsboththefuturebehaviorofthesys temandtheprecisionofthefuturestateandparame terestimation .Thisisthewell knowndualeffect[1] ,andoptimalco…     

分解刚性大系统数值仿真并行算法

针对一类分解的刚性大系统，根据系统分割的思想，提出了组合ＲＫ－Ｒｏｓｅｎｂｒｏｃｋ方法，将方法分割和系统分割的思想相结合，构造了并行组合方法。对于提出的并行算法，比较系统地研究了算法的构造以及它们的收敛性和数值稳定性，并在微机和多处理机上进行了数值仿真试验。     

Analysis of wire antennas mounted on large perfectly conducting platforms using MLFMA

The electric field integral equation (EFIE) combined with the multilevel fast multipole algorithm (MLFMA) is applied to analyze the radiation and impedance properties of wire antennas mounted on complex conducting platforms to realize fast, accurate solutions. Wire, surface and junction basis functions are used to model the current distribution on the object. Application of MLFMA reduces memory requirement and computing time compared to conventional methods, such as method of moment (MOM), especially for the antenna on a large-sized platform. Generalized minimal residual (GMRES) solver with incomplete LU factorization preconditioner using a dual dropping strategy (ILUT) is applied to reduce the iterative number. Several typical numerical examples are presented to validate this algorithm and show the accuracy and computational efficiency.     

解析与数值的意义及所描述的世界

基本科学规律一般指动力学规律即状态时间变化的微观规律,呈现为“边界条件＋动力学方程”形式。动力学方程是潜无限意义下的微分方程,少数简单情况下有解析解,初等连续函数形式的解析解描述的是一个确定性、连续性的世界;多数情况下没有解析解,那是一个不确定性和非线性放大机制并存的世界;潜无限动力学方程不能完全描述的是实无限的连续性世界。在运动学层面,无论有无解析解也无论存不存在动力学方程,都可以用数值方法研究动力学现象的运动学行为,数值解描述的是有限性、确定性、离散性、历史性的世界。     

SIMPLE COMPUTING OF THE CUSTOMER LIFETIME VALUE:A FIXED LOCAL-OPTIMAL POLICY APPROACH

In this paper,we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value.The method is developed for a class of ergodic controllable finite Markov chains.We propose an approach based on a non-converging state-value function that fluctuates（increases and decreases） between states of the dynamic process.We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy.Then,we provide an analytical formula for the numerical realization of the fixed local-optimal strategy.We also present a second approach based on linear programming,to solve the same problem,that implement the c-variable method for making the problem computationally tractable.At the end,we show that these two approaches are related：after a finite number of iterations our proposed approach converges to same result as the linear programming method.We also present a non-traditional approach for ergodicity verification.The validity of the proposed methods is successfully demonstrated theoretically and,by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.     

非线性回归模型辨识的混合计算智能算法

通过定义牛顿算子、选择算子、混合数据结构以及适应度，得到可结合遗传算法和牛顿法两者长处，既有较快收敛性，又能以较大概率求得全局解（一致收敛估计）的非线性参数辨识算法。数值计算结果表明该方法显著优于遗传算法和牛顿法。     

计算实验方法与复杂系统行为分析和决策评估

本文提出计算实验方法的基本思想、概念和方法,并讨论计算仿真与计算实验的关系和异同之处,以及基于涌现的实验观察和解释方法。计算实验是计算仿真随着计算技术和分析方法的进一步发展而必须迈上的一个更高的台阶,是弥补很难甚至无法对复杂系统进行实验之不足的一种有效手段,也是分析复杂行为和评估各种决策效果的一种可行方式。     

三维气流数值仿真中悬浮边界面处理技术的研究

气流组织是空调房间内空气的分布、流动形式,主要反映在气流的温度、湿度、气流速度和清洁度等指标,是否符合行业标准规定的空调房间的要求.气流组织可以通过数值计算理论、计算机仿真技术给予实现.以一个典型的变风量中央空调房间为研究基础,以该房间内的送、回风口边界面为研究实例,通过分析、研究悬浮在房间立体内的送、回风口的数值仿真方法,运用实体造型技术,设计出在房间立体与悬浮边界面之间的拓扑关系,使两者成为一体.然后该处理技术经过数值仿真实例的验证证明是合理的、可行的.     

Chaotification of a continuous stable complex network via impulsive control

A method is proposed to chaotify a class of complex networks via impulsive control, when the orbits of the impulsive systems are con?ned in a bounded area. Based on computing the largest Lyapunov exponent, theoretical results and algorithmic analysis are given in details. Finally, numerical simulations are presented to illustrate the effectiveness of the method.     

Improving the Estimations of VaR-GARCH Using Genetic Algorithm

1　 IntroductionIn recent years,well-publicized losses suffered by some institutions such as Natwest,Baring Bank,Metallgesellschaft,and Orange County have brought risk management tothe core of policy making and public discussion,and there has a widespread call for betterquantification of financial market risk facing regulations and financial society.At theforefront of this clamor for a standardizaed risk measure has been Value at Risk( Va R) [1～ 5] .Va R is defined as the expected loss on…