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2010年工作年报



一、机构设置和聘任工作
二、科学研究方向、科研项目和经费
三、科学研究成果
四、学术活动
五、学科建设和人才培养
六、工作环境及实验室建设
七、2010年论文摘要

一、机构设置和聘任工作
1.根据《上海高校计算科学E—研究院建设总体规划书》、《上海高校计算科学E—研究院建设发展规划书(2008年-2010年)》和《上海高校计算科学E—研究院管理章程》等文件,制订和执行2010年度工作计划。
2.郭本瑜教授为首席研究员,并聘请下列专家为特聘研究员:
  • 程  晋 复旦大学教授
  • 黄建国 上海交通大学教授
  • 岳荣先 上海师范大学教授
  • 王元明 华东师范大学教授
  • 徐承龙 同济大学教授
  • 田红炯 上海师范大学教授
  • 王中庆 上海师范大学教授
  • 苏仰锋 复旦大学教授
  • 郭  谦 上海师范大学副教授
  • 上海师范大学彭丽副教授、徐东博士、郭玲博士和徐海燕博士为上海高校计算科学E—研究院青年培育人员。
3.由下列专家组成学术委员会:
  • 主任:石钟慈 中国科学院院士
  • 委员:林  群 中国科学院院士
  • 姜礼尚 同济大学教授
  • 郭本瑜 上海师范大学教授
  • 张伟江 上海交通大学教授
  • 吴宗敏 复旦大学教授
  • 王翼飞  上海大学教授
  • 香港城市大学王世全教授为研究院顾问。
4.田红炯教授兼任业务秘书,谢丽同志任行政秘书。
二、科学研究方向、科研项目和经费
1.根据E—研究院科学研究方向,制订并资助2010年度研究课题,承担国家和上海市其它科研项目,积极申请新的科研项目。
2.主要研究方向:
  • 科学与工程中的高性能算法
  • 数学物理中的反问题计算方法
  • 复杂结构和复杂物理现象的数学模型及算法
  • 随机模型和随机算法
  • 常微分方程的高效数值解法
  • 生物与材料科学中的数学模型及其算法
  • 大型和非线性代数问题的快速算法
3.本年度资助下列研究课题
  • 郭本瑜 无界区域问题和外部问题的高精度算法      
  • 程  晋 数学物理反问题的理论及其数值计算        
  • 黄建国 组合弹性结构的有限元方法研究       
  • 岳荣先 高维积分的拟蒙特卡洛新算法及其误差分析         
  • 田红炯 常微分系统的数值方法及其应用               
  • 徐承龙 信用风险分析及产品定价中的随机与确定性算法    
  • 王元明 拟线性抛物和椭圆型方程的高精度紧致差分方法     
  • 王中庆 数学物理问题的高精度算法
  • 苏仰锋 非线性特征值问题的理论分析及计算             
4.特聘研究员承担了17项国家和上海市科研项目,本年度到达总经费181.1万元。
A.国家科研项目9个,本年度到达经费58.8万元。
  • 郭本瑜   国家自然科学基金,谱方法若干问题研究。
  • 程  晋   国家基金委中美合作项目,数学物理方程的反问题及其应用。
  • 程  晋   国家基金委国际合作交流,中德芬三方反问题研讨会。
  • 黄建国   国家自然科学基金,组合弹性结构的自适应有限元方法研究。
  • 徐承龙   国家973计划项目子课题,信用风险分析和信用衍生产品定价。
  • 王中庆   国家自然科学基金,外部问题的高精度算法及其应用。
  • 王中庆   国家973计划项目子课题,高性能科学计算研究。
  • 苏仰锋   国家自然科学基金,非线性特征值问题的理论分析及计算。
  • 郭  谦   国家自然科学基金,癌症研究关键问题中的分歧与计算方法研究。
B.上海市及教育部科研项目8个,本年度到达经费122.3万元。
  • 郭本瑜   国家教育部博士点基金,谱方法中的若干前沿问题研究。
  • 郭本瑜   上海市科技攻关项目,高性能计算方法研究。
  • 程  晋   国家外专局和教育部111引智计划,复旦大学现代应用数学创新引智基地。
  • 程  晋   中国人民解放军总装备部咨询项目。
  • 王中庆   上海市教委曙光计划,Neumamm边值问题和外部问题的谱方法以及时间方向的配置法。
  • 王元明   上海市自然科学基金,拟线性边值问题的高精度紧有限差分方法。
  • 郭  谦   上海市自然科学基金,癌症研究关键问题中的分歧与计算方法研究。
  • 郭  谦   上海市教委科研创新项目,前列腺癌治疗模型中的数值模拟方法。
5.最近申请并获准主持5个国家和上海市科研项目(2011年开始执行),总经费162万元。
  • 程  晋     国家973计划项目子课题,适应于千万亿次科学计算的新型计算模式。
  • 田红炯     国家自然科学基金,常微分方程初值问题若干新算法及其应用。
  • 岳荣先     国家自然科学基金,随机系数回归模型的最优设计与稳健设计。
  • 田红炯     上海市教委科研创新重点项目,中立型微分代数系统的计算方法及其数值分析。
  • 岳荣先     上海市教委科研创新重点项目:随机系数重复测量模型的试验设计若干问题研究。
 
三、科学研究成果
本年度在奇异和无界区域问题的高精度数值方法、数学物理反问题的数值解法、组合弹性结构的数学模型和计算、常微分方程的高效数值方法、随机化伪Monte-Carlo方法及其应用和非线性特征值问题的理论分析及计算等方面取得了一批研究成果,在国内外重要学术刊物上发表了31篇论文,其中某些结果是原创性的,有关结果引起国内、外同行的高度评价。

1.科学与工程中的高性能算法(郭本瑜,王中庆)
  • 引入了一类新的广义Jacobi有理正交函数系,建立了相应的正交逼近理论,并应用于Sine-Gordon, Klein-Gordon和Fisher等方程的谱方法,它们拟合各种边界条件。
  • 提出了二维四阶外部问题的Laguerre-Legendre混合谱方法,建立了有关的逼近理论,证明了谱格式的收敛性。数值结果显示了该方法具有谱精度。
  • 研究了凸四边形上的谱方法,建立了有关的拟正交逼近理论。同时研究了凸多角型区域上的谱方法,拓广了谱方法的应用。
  • 构造了三维外部问题的球面调和-广义Laguerre混合拟谱方法。
  • 提出了精确满足混合边界条件的新配置方法,建立了广义Gauss- Lobatto-Legendre-Birhoff类型的求积公式,并应用于Helmholtz方程计算。
  • 从不同角度研究了广义Hermite函数的逼近性质,有效地简化了理论分析,并将上述结果应用于Ginzburg–Landau方程等有关问题的计算。
有关论文:
[1]Benyu Guo and Yonggang Yi, Generalized Jacobi rational spectral method and its applications, J. Sci. Comp., 43(2010), 201-238.
[2]Benyu Guo and Tianjun Wang, Composite Laguerre-Legendre spectral method for exterior problems, Adv. Comp. Math., 32(2010), 393-429.
[3]Benyu Guo and Hongli Jia, Spectral method on quadrilaterals, Math. Comp., 79(2010), 2237-2264.
[4]Benyu Guo and Tianjun Wang, Composite Laguerre-Legendre spectral method for fourth-order exterior problems, J. Sci. Comp., 44(2010), 255-285.
[5]Zhongqing Wang, Rong Zhang and Benyu Guo, Spherical harmonic- generalized Laguerre pseudospectral method for three dimensional exterior problems, Inter. J.  Comp. Math., 87(2010), 2123-2142.
[6]Zhongqing Wang and Lilian Wang, A collocation method with exact imposition of mixed boundary conditions, J. Sci. Comp., 42(2010), 291-317.
[7]Xinmin Xiang and Zhongqing Wang, Generalized Hermite spectral method and its applications to problems in unbounded domains, SIAM J. Numer. Anal., 48(2010), 1231-1253.

2.数学物理反问题的理论和数值方法(程晋)
  • 在有关热传导的反问题方面取得了一些重要的进展,解决了一系列的重要难题,取得了2项日本发明专利。
  • 研究一类具有重要实际背景和理论研究价值时间序列的数据聚类分析。基于正则化方法,引入一类正则化算子使得极小化泛函的解可以更准确地刻画数据的聚类中心随时间变化的趋势,并应用该方法分析了20年来云南地区的水准形变数据,寻找状态转移与地震之间的关系。
有关论文:
[1]Yanbin Wang, Jin Cheng, Junichi Nakagawa and Masahiro Yamamoto, A numerical method for solving the inverse heat conduction problem without initial value, Inv. Probl. Sci. Eng., 18 (2010), 655–671.

3.组合弹性结构问题的有限元方法(黄建国)
  • 建立求解Kirchhoff板弯曲问题的一类新型LCDG方法,建立算法误差分析理论并提供数值模拟结果。该方法只要待选的参数大于零即有效,便于工程实用。
  • 提出离散纵标间断Galerin方法(DODG)数值求解三维情形Radiative Transfer Eqation(RTE)问题,并系统建立算法误差分析理论并提供数值模拟结果。
  • 系统建立Kirchhoff板和组合弹性结构振动问题的有限元算法和误差估计理论并进行数值模拟。
  • 给出带约束矩阵方程及其最小二乘法的统一算法与应用。
有关论文:
[1]Weimin Han, Jianguo Huang and Joseph A. Eichholtz, Discrete-ordinate discontinuous Galerkin method for solving the radiative transfer equation, SIAM J. Sci. Comp., 32(2010), 477-497.
[2]Ling Guo and Jianguo Huang, Dynamical analysis of Kirchhoff plates by an explicit time integration Morley element method, J. Comp. Appl. Math., 234(2010), 2483-2492.
[3]Ling Guo and Jianguo Huang, Adini Q1-P3 FEM for general elastic multi-structure problems, Numer. Meth. Part. Diff. Equa., 2010, 6, DOI 10.1002/num.20571.
[4]Jianguo Huang, Xuehai Huang and Weimin Han, A new C  discontinuous Galerkin method for Kirchhoff plates, Comp. Meth. Appl. Mech. Engr., 199(2010), 1446-1454.
[5]JianguoHuang and Liwei Nong, An iterative algorithm for solving a finite-dimensional linear operator equation T(x) = f with applications, Linear Alge. Appl., 432(2010), 1176-1188.
[6]Junjiang Lai, Jianguo Huang and Zhongci Shi, Vibration analysis for elastic multi-beam structures by the C -continuous time-stepping finite element method, Int. J. Numer. Meth. Biomed. Eng., 26(2010), 205-233.
[7]Junjiang Lai, Jianguo Huang and Zhongci. Shi, A lumped mass finite element method for vibration analysis of elastic plate-plate structures, Sci. China Ser. A., 53(2010), 1453-1474.

4.常微分方程的数值方法(郭本瑜、王中庆、田红炯)
  • 提出了一阶常微分动力系统的Legendre-Gauss-Lobatto新配置法,二阶常微分动力系统的Laguerre- Gauss新配置法,及一类时滞系统的Legendre-Gauss新配置法,该方法计算稳定并具有谱精度。
  • 研究中立型微分代数方程的渐近稳定性理论,给出了线性多步法为数值渐近稳定的充要条件。
  • 提出中立型微分代数方程渐近稳定的一个等价条件,给出了Runge-Kutta法为数值渐近稳定的充要条件。
有关论文:
[1]Benyu Guo and Zhongqing Wang, A spectral collocation method for solving initial value problems of first order ordinary differential equations, Disc. Cont. Dyna. Syst. B, 14(2010), 1029-1054.
[2]Zhongqing Wang and Lilian Wang, A Legendre-Gauss collocation method for nonlinear delay differential equations, Disc. Cont. Dyna. Syst. B, 13(2010), 685-708.
[3]Mohammad Taghi Darvishi, Farzad Khani, Ali Mohammad Godarzi and Hongjiong Tian, Symmetric modified AOR method to solve systems of linear equations, J. Appl. Math. Comp., DOI 10.1007/s12190-010-0387-6.

5.随机伪蒙特卡罗方法的理论与应用(岳荣先)
  • 对于具有滑动平均过程MA(q)结构随机误差的近似线性回归模型,分别利用再生核Hilbert空间方法和Bayes方法建立最优设计准则,给出构造这类最优设计的算法,并将经典最优设计与指定相关结构下的最优设计进行数值比较。
  • 对于具有s个因子(解释变量)的非参数响应曲面预测模型,在Bayes框架下研究等水平情况下的均匀型设计,建立了该准则与正交性和混杂性度量的关系,并给出该准则函数的下界。
  • 对一类分级有序的多响应线性回归模型,证明最优设计与响应向量的协方差矩阵无关,并对回归函数分别为三角函数和Haar小波函数的回归模型给出了相应的最优设计。
  • 讨论两响应线性Haar小波模型的最优试验设计问题,给出同时具有D-, A-和Q-最优性, 并且与两响应变量的协方差阵无关的设计。
  • 利用广义P值和广义置信区间的概念构造含有三个随机效应的Panel数据模型中方差分量的几种新的精确检验和置信区间,并讨论它们在尺度变换下的不变性,通过模拟给出检验的功效和置信区间的覆盖率。模拟结果表明广义P值理论方法是灵活而有效的。
有关论文:
[1]Rongxian Yue and Xiaodong Zhou, Bayesian robust designs for linear models with possible bias and correlated errors, Metrika,71(2010), 1–15.
[2]Rongxian Yue and Kashinath Chatterjee, Bayesian U-type design for nonparametric response surface prediction, Metrika, 72(2010), 219–231.
[3]Rongxian Yue and Xin Liu,  -optimal designs for a hierarchically ordered system of regression models, Comp. Stat. Data Anal., 54(2010), 3458–3465.
[4]Rongxian Yue and Xiaodong Zhou, Robust designs for models with possible bias and correlated errors, Appl. Math. J. Chin. Univ., 25(2010), 307-317.
[5]刘欣,岳荣先,两响应Haar小波回归模型最优设计, 应用概率统计,26(2010),151–158。
[6]程靖,王松桂,岳荣先,Panel数据模型中方差分量的精确检验, 应用概率统计, 26(2010),89–98。

6.非线性初(边)值问题的高精度有限差分方法(王元明)
  • 对一类非线性反应扩散方程组的有限差分解给出了数值分析, 包括单调算法及长时间解的渐近收敛性。
  • 建立了非局部边值问题的一些定性理论,为构造高阶紧有限差分方法奠定了理论基础。
  • 构造了拟线性两点边值问题的四阶紧有限差分方法,拓广了高阶紧有限差分方法的应用范围。
  • 提出了二维抛物边值问题的高阶紧LOD (locally one-dimensional) 差分方法, 为高阶紧差分方法的应用开辟了新途径。
有关论文:
[1]Yuanming Wang and Yuan Gong, Numerical solutions of a nonlinear reaction-diffusion system, Inter. J. Comp. Math., 87 (2010), 1975–2002.
[2]Chia Ven Pao and Yuanming Wang, Nonlinear fourth-order elliptic equations with nonlocal boundary conditions, J. Math. Anal. Appl., 372(2010), 351–365.
[3]Yuanming Wang, On 2nth-order nonlinear multi-point boundary value problems, Math. Comp. Model., 51 (2010), 1251–1259.
[4]Yuanming Wang, The iterative solutions of 2nth-order nonlinear multi-point boundary value problems, Appl. Math. Comp., 217 (2010), 2251–2259.

7.金融衍生物的偏微分方程定价理论与计算(徐承龙)
  • 对一类随机波动率的衍生产品定价设计了一种控制变量蒙特卡罗加速算法,使得计算效率与简单蒙特卡罗相比较可提高约100倍(一般模拟试验1000次,计算精度可精确到相对误差百分之1%)。
  • 设计了一种基于主成份作为控制变量的Monte  Carlo 加速算法,计算效果满意,并可推广到多维问题。
有关论文:
[1]Junmei Ma,Chenglong Xu, An efficient control variate method for pricing variance derivatives, J. Comp. Appl. Math., 235 (2010), 108-119.
[2]徐承龙,徐晓芸,CDO模型的市场重构与LDG分布, 同济大学学报, 38(2010),1496-1500。

8.非线性特征值问题的理论分析及计算(苏仰锋)
  • 研究二次特征值问题的保结构变换,建立保结构变换的基础理论,并给出保结构变换的构造和数值稳定性等。
  • 提出大规模带低秩阻尼的非线性特征值问题的一类非常有效的算法,并对一般的带低秩阻尼的非线性特征值问题也给出了一个有效的算法。

9.生物数学模型及其算法(郭谦)
  • 建立抑制剂治疗荷尔蒙依赖型细胞突变的前列腺癌间歇治疗模型,对突变抑制剂的影响做了详尽的动力学分析。
有关论文:
[1]Youshan Tao, Qian Guo and Kazuyuki Aihara, A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor, J. Nonli. Sci., 20(2010), 219-240.
四、学术活动
遵循研究院管理章程进行日常学术活动,举办或合办了一些国内或国际学术会议,提升上海高校计算科学E-研究院的影响力。
1.日常学术活动
  • 每月召开特聘研究员工作会议,交流科学研究工作并部署下一步研究工作。
  • 每月举办一次面向全市的学术报告会,由特聘研究员或院外专家介绍科学计算的新进展。
  • 邀请著名专家来校参加计算数学学术年活动并开设学术讲座。
  • 邀请10余名国内、外专家来研究院讲学或合作研究。
  • 研究院成员参加国际、国内学术会议10多人次,并作邀请报告或报告。多名研究员到国外或境外讲学或短期合作研究。
2.举办或合办国内、外学术会议
  • 2010年6月,   与复旦大学联合举办“International Conference on Scattering
  • Theory and its Numerical Algorithms”。
  • 2010年6月,   与复旦大学、浙江理工大学联合举办“数学物理反问题及
  • 其应用”研讨会。
  • 2010年6月,   与上海金融学院联合举办第十九届“矩阵与统计”国际学
  • 术会议。
  • 2010年11月,  与上海大学联合举办上海市第六届“科学与工程中的计算
  • 方法”研讨会。
五、学科建设和人才培养
根据上海高校E—研究院的建设宗旨,加速培养上海市各高校计算数学专业的学术带头人和高水平专业人才,促进有关高校计算数学学科的建设。
1.申请数学一级学科博士点,已被上海市学位委员会批准并上报。
2.研究院成员共指导了5名博士后,22名博士生(其中毕业5名)。指导国内访问学者2名。
3.程晋教授被聘请为国家973计划项目研究成员。  
六、工作环境及实验室建设
加强上海高校计算科学E—研究院和“科学计算”上海高校重点实验室建设。
1.拥有SGI工作站(32个CPU,内存为16GB,硬盘容量达到730GB)。
2.购置了7台多核高性能计算机及配套设施。
3.订购了多种数学学科电子期刊数据库,已能满足下载主要国际学术杂志论文的需要。
七、2010年论文摘要
Panel数据模型中方差分量的精确检验
程靖,王松桂,岳荣先
应用概率统计,26(2010),89–98.
摘要
本文利用广义P值和广义置信区间的概念构造含有三个随机效应的Panel数据模型中方差分量的几种新的精确检验和置信区间,并讨论它们在尺度变换下的不变性.通过模拟给出检验的功效和置信区间的覆盖率。模拟结果表明,广义P值理论方法应用于含有冗余参数的Panel数据模型参数检验问题是灵活而有效的.

Symmetric modified AOR method to solve systems of linear equations
Mohammad Taghi Darvishi, Farzad Khani, Ali Mohammad Godarzi and Hongjiong Tian
J. Appl. Math. Comp., DOI: 10.1007/s12190-010-0387-6
Abstract
We propose a class of symmetric modified accelerated overrelaxation (SMAOR) methods for solving large sparse linear systems. The convergence region of the method has been investigated. Numerical examples indicate that the SMAOR method is better than other methods such as accelerated overrelaxation (AOR) and modified accelerated overrelaxation (MAOR) methods, since the spectral radius of iteration matrix in SMAOR method is less than that of the other methods. Also, we apply the method to solve a real boundary value problem.

Spectral method on quadrilaterals
Benyu Guo and Hongli Jia
Math. Comp., 79(2010), 2237-2264.
Abstract
In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schemes for two model problems and prove their spectral accuracy in Jacobi weighted Sobolev space. Numerical results coincide well with the analysis. We also investigate the spectral method on convex polygons whose solutions possess spectral accuracy. The approximation results of this paper are also applicable to other problems.

Composite Laguerre-Legendre spectral method for exterior problems
Benyu Guo and Tianjun Wang
Adv. Comp. Math., 32(2010), 393-429.
Abstract
In this paper, we propose a composite Laguerre-Legendre spectral method for two-dimensional exterior problems. Results on the composite Laguerre-Legendre approximation, which is a set of piecewise mixed approximations coupled with domain decomposition, are established. These results play important roles in the related spectral methods for exterior problems. As examples of applications, the composite spectral schemes are provided for two model problems, with the convergence analysis. An efficient implementation is described. Numerical results demonstrate the spectral accuracy in space.

Composite Laguerre-Legendre spectral method for fourth-order exterior problems
Benyu Guo and Tianjun Wang
J. Sci. Comp., 44(2010), 255-285.
Abstract
In this paper, we investigate composite Laguerre-Legendre spectral method for fourth-order exterior problems. Some results on composite Laguerre-Legendre approximation are established, which is a set of piecewise mixed approximations coupled with domain decomposition. These results play an important role in spectral method for fourth-order exterior problems with rectangle obstacle. As examples of applications, composite spectral schemes are provided for two model problems, with convergence analysis. Efficient algorithms are implemented. Numerical results demonstrate their high accuracy, and confirm theoretical analysis well.

A spectral collocation method for solving initial value problems of first order ordinary differential equations
Benyu Guo and Zhongqing Wang
Disc. Cont. Dyna. Syst. B, 14(2010), 1029-1054.
Abstract
We propose a spectral collocation method for solving initial value problems of first order ODEs, based on the Legendre-Gauss-Lobatto  interpolation. This method is easy to be implemented and possesses the spectral accuracy.  We also develop a multi-step version of this process, which is very available for long-time calculation. Numerical results demonstrate the high accuracy of suggested algorithms and coincide well with the theoretical analysis.

Generalized Jacobi rational spectral method and its applications
Benyu Guo and Yonggang Yi
J. Sci. Comp., 43(2010), 201-238.
Abstract
We introduce an orthogonal system on the whole line, induced by the generalized Jacobi functions. Some results on the generalized Jacobi rational approximation are established, which play important roles in the related spectral methods. As examples of applications, the rational spectral schemes are proposed for sine-Gordon, Klein-Gordon and Fisher equations, with the convergence analysis. Numerical results demonstrate their efficiency.

Dynamical analysis of Kirchhoff plates by an explicit time integration Morley element method
Ling Guo and Jianguo Huang
J. Comp. Appl. Math., 234(2010), 2483-2492.
Abstract
An explicit time integration finite element method is proposed to investigate dynamical analysis of Kirchhoff plates, where the Morley element is used for spatial discretization and the second-order central scheme for time discretization. Certain error estimates in the energy norm are achieved. A number of numerical results are included to show computational performance of the method.

Adini Q1-P3 FEM for general elastic multi-structure problems
Ling Guo and Jianguo Huang
Numer. Meth. Part. Diff. Equa., 2010, DOI 10.1002/num.20571.
Abstract
An Adini-Q1-P3 finite element method is introduced to solve general elastic multi-structure problems, where displacements on bodies, longitudinal displacements on plates, longitudinal displacements and rotational angles on rods are discretized by conforming linear (bilinear or trilinear) elements, and transverse displacements on plates and rods are discretized by Adini elements and Hermite elements of third order, respectively. The unique solvability and optimal error estimates in the energy norm are established for the discrete method, whose numerical performance is illustrated by some numerical examples.

Discrete-ordinate discontinuous Galerkin methods fo solving the radiative transfer equation
Weimin Han, Jianguo Huang and Joseph A. Eichholtz
SIAM J. Sci. Comp., 32(2010), 477-497.
Abstract
The radiative transfer equation (RTE) occurs in a wide variety of applications.  In this paper, we study discrete-ordinate discontinuous Galerkin methods for solving the RTE.  The numerical methods are formed in two steps.  In the first step, the discrete ordinate technique is applied to discretize the integral operator for the angular variable, resulting in a semi-discrete hyperbolic system.  In the second step, the spatial discontinuous Galerkin method is applied to discretize the semi-discrete system.  A stability and error analysis is performed on the numerical methods.  Some numerical examples are included to demonstrate the convergence behavior of the methods.

A new C  discontinuous Galerkin method for Kirchhoff plates
Jianguo Huang, Xuehai Huang and Weimin Han
Comp. Meth. Appl. Mech. Engr., 199(2010), 1446-1454.
Abstract
A general framework of constructing C  discontinuous Galerkin (CDG) methods is developed for solving the Kirchhoff plate bending problem, following some ideas by Cockburn. The numerical traces are determined based on a discrete stability identity, which lead to a class of stable CDG methods. A stable CDG method, called the LCDG method, is particularly interesting in our study. It can be viewed as an extension to fourth-order problems of the LDG method. For this method, optimal order error estimates in certain broken energy norm and  -norm are established. Some numerical results are reported, confirming the theoretical convergence orders.

An iterative algorithm for solving a finite-dimensional linear operator
equation T(x)=f with applications
JianguoHuang and Liwei Nong
Linear Alge. Appl., 432(2010), 1176-1188.
Abstract
This paper proposes an iterative algorithm for solving a general finite-dimensional linear operator equation T(x)=f and demonstrates that it will get the exact solution within a finite number of iteration steps. This algorithm unifies all the iterative methods in several papers and provides an iterative method for solving an inverse problem related to Hermitian-generalized Hamiltonian matrices.

Vibration analysis for elastic multi-beam structures by the C0-continuous time-stepping finite element method
Junjiang Lai, Jianguo Huang and Zhongci Shi
Int. J. Numer. Meth. Biomed. Engr., 26(2010), 205-233.
Abstract
Some C0-continuous time-stepping finite element method is proposed for investigating vibration analysis of elastic multi-beam structures. In the time direction, the C0-continuous Galerkin method is used to discretize the generalized displacement field. In the space directions, the longitudinal displacements and rotational angles on beams are discretized using conforming linear elements, while the transverse displacements on beams are discretized by the Hermite elements of third order. The error of the method in the energy norm is proved to be O(h+k3), where h and k denote the mesh sizes of the subdivisions in the space and time directions, respectively. The finite difference analysis in time is developed to discuss the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low-frequency regime. The method has also been extended to study some nonlinear problems. A number of numerical tests are included to illustrate the computational performance of the method.

A lumped mass finite element method for vibration analysis of elastic plate-plate structures
Junjiang Lai, Jianguo Huang and Zhongci Shi
Sci. China Ser. A, 53(2010), 1453-1474.
Abstract
The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate structures. In the space directions, the longitudinal displacements on plates are discretized by conforming linear elements, and the transverse displacements are discretized by the Morley element. By means of the second order central difference for discretizing the time derivative and the technique of lumped masses, a fully discrete lumped mass finite element method is obtained, and two approaches to choosing the initial functions are also introduced. The error analysis for the method in the energy norm is established, and some numerical examples are included to validate the theoretical analysis.

两响应Haar小波回归模型最优设计
刘欣,岳荣先
应用概率统计,26(2010),151–158.
摘要
本文讨论两响应线性Haar小波模型的最优试验设计问题。假定每个响应变量与自变量之间的回归关系可以用一个线性小波多项式表示。本文给出一个设计,它同时具有D-,A-和Q-最优性,并且与两响应变量的协方差阵无关。

An efficient control variate method for pricing variance derivatives
Junmei Ma and Chenglong Xu
J. Comp. Appl. Math., 235 (2010), 108-119.
Abstract
This paper studies the pricing of variance swap derivatives with stochastic volatility by the control variate method. A closed form solution is derived for the approximate model with deterministic volatility, which plays the key role in the paper, and an efficient control variate technique is therefore proposed when the volatility obeys the log-normal process. By the analysis of moments for the underlying processes, the optimal volatility function in the approximate model is constructed. The numerical results show the high efficiency of our method; the results coincide with the theoretical results. The idea in the paper is also applicable for the valuation of other types of variance swap, options with stochastic volatility and other financial derivatives with multi-factor models.

Nonlinear fourth-order elliptic equations with nonlocal boundary conditions
Chia Ven Pao and Yuanming Wang
J. Math. Anal. Appl., 372(2010), 351–365.
Abstract
This paper is concerned with a class of fourth-order nonlinear elliptic equations with nonlocal boundary conditions, including a multi-point boundary condition in a bounded domain of Rn. Also considered is a second-order elliptic equation with nonlocal boundary condition, and the usual multi-point boundary problem in ordinary differential equations. The aim of the paper is to show the existence of maximal and minimal solutions, the uniqueness of a positive solution, and the method of construction for these solutions. Our approach to the above problems is by the method of upper and lower solutions and its associated monotone iterations. The Monotone iterative schemes can be developed into computational algorithms for numerical solutions of the problem by either the finite difference method or the finite element method.

A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor
Youshan Tao, Qian Guo and Kazuyuki Aihara
J. Nonli. Sci., 20(2010), 219–240.
Abstract
This paper extends Jackson’s model describing the growth of a prostate tumor with hormone therapy to a new one with hypothetical mutation inhibitors. The new model not only considers the mutation by which androgen-dependent (AD) tumor cells mutate into androgen-independent (AI) ones but also introduces inhibition which is assumed to change the mutation rate. The tumor consists of two types of cells (AD and AI) whose proliferation and apoptosis rates are functions of androgen concentration. The mathematical model represents a free-boundary problem for a nonlinear system of parabolic equations, which describe the evolution of the populations of the above two types of tumor cells. The tumor surface is a free boundary, whose velocity is equal to the cell’s velocity there. Global existence and uniqueness of solutions of this model is proved. Furthermore, explicit formulae of tumor volume at any time t are found in androgen-deprived environment under the assumption of radial symmetry, and therefore the dynamics of tumor growth under androgen-deprived therapy could be predicted by these formulae. Qualitative analysis and numerical simulation show that controlling the mutation may improve the effect of hormone therapy or delay a tumor relapse.

A numerical method for solving the inverse heat conduction problem without initial value
Yanbin Wang, Jin Cheng, Junichi Nakagawa and Masahiro Yamamoto
Inv. Prob. Sci. Eng. 18 (2010), 655–671.
Abstract
We consider the inverse heat conduction problem for the one-dimensional heat equation, where we are requested to determine a boundary value at one end of a spatial interval over a time interval and an initial value by means of Cauchy data at another end. By the existing theory we can prove the uniqueness in determining both a boundary value and an initial value, and our method does not require any initial value. We test our numerical method and show stable numerical reconstruction.

On 2nth-order nonlinear multi-point boundary value problems
Yuanming Wang
Math. Comp. Model., 51 (2010), 1251–1259.
Abstract
This paper is concerned with the existence and uniqueness of a solution for a class of 2nth-order nonlinear multi-point boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone condition on the nonlinear function. A sufficient condition for the uniqueness of a solution is given. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. Two examples are presented to illustrate the results. Some numerical results are given. All the conclusions are directly applicable to the finite difference solution of the corresponding ordinary differential system.

The iterative solutions of 2nth-order nonlinear multi-point boundary value problems
Yuanming Wang
Appl. Math. Comp., 217 (2010), 2251–2259.
Abstract
The aim of this paper is to investigate the existence of iterative solutions for a class of 2nth-order nonlinear multi-point boundary value problems. The multi-point boundary condition under consideration includes various commonly discussed boundary conditions, such as three- or four-point boundary condition, (n+2)-point boundary condition and 2(n- m)-point boundary condition. The existence problem is based on the method of upper and lower solutions and its associated monotone iterative technique. A monotone iteration is developed so that the iterative sequence converges monotonically to a maximal solution or a minimal solution, depending on whether the initial iteration is an upper solution or a lower solution. Two examples are presented to illustrate the results.

Numerical solutions of a nonlinear reaction-diffusion system
Yuanming Wang and Yuan Gong
Int. J. Comp. Math., 87 (2010), 1975–2002.
Abstract
This paper is concerned with finite difference solutions of a coupled system of nonlinear reaction-diffusion equations. The investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. The existence and uniqueness of a non-negative finite difference solution and three monotone iterative algorithms for the computation of the solutions are given. It is shown that the time-dependent problem has a unique non-negative solution, whereas the steady-state problem may have multiple non-negative solutions depending on the parameters in the problem. The different non-negative steady-state solutions can be computed from the monotone iterative algorithms by choosing different initial iterations. Also discussed is the asymptotic behaviour of the time-dependent solution in relation to the steady-state solutions. The asymptotic behaviour result gives some conditions ensuring the convergence of the time-dependent solution to a positive or semitrivial non-negative steady-state solution. Numerical results are given to demonstrate the theoretical analysis results.

A collocation method with exact imposition of mixed boundary conditions
Zhongqing Wang and Lilian Wang
J. Sci. Comp., 42(2010), 291-317.
Abstract
In this paper, we propose a natural collocation method with exact imposition of mixed boundary conditions based on a generalized Gauss-Lobatto-Legendre-Birhoff quadrature rule that builds in the underlying boundary data. We provide a direct construction of the quadrature rule, and show that the collocation method can be implemented as efficiently as the usual collocation scheme for PDEs with Dirichlet boundary conditions. We apply the collocation method to some model PDEs and the time-harmonic Helmholtz equation, and demonstrate its spectral accuracy and efficiency by various numerical examples.

A Legendre-Gauss collocation method for nonlinear delay differential equations
Zhongqing Wang and Lilian Wang
Disc. Cont. Dyna. Syst. B, 13(2010), 685-708.
Abstract
In this paper, we introduce an efficient Legendre-Gauss collocation method for solving nonlinear delay differential equations with variable delay. We analyze the convergence of the single-step and multi-domain versions of the proposed method, and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. We also make numerical comparison with other methods.

Spherical harmonic-generalized Laguerre pseudospectral method for three dimensional exterior problems
Zhongqing Wang, Rong Zhang and Benyu Guo
Inter. J. Comp. Math., 87(2010), 2123-2142.
Abstract
In this paper, we develop the mixed pseudospectral method for three-dimensional exterior problems. Some basic results on the mixed spherical harmonic-generalized Laguerre interpolation are established, which play important roles in the related pseudospectral methods. As examples, we provide the mixed pseudospectral schemes for two exterior problems with convergence analysis. Numerical results demonstrate the efficiency of this approach.

Generalized Hermite spectral method and its applications to problems in unbounded domains
Xinmin Xiang and Zhongqing Wang
SIAM J. Numer. Anal., 48(2010), 1231-1253.
Abstract
In this paper, we develop a spectral method based on generalized Hermite functions with weight  . We also establish some basic results on generalized Hermite orthogonal approximations, which play an important role in spectral methods. As examples, the generalized Ginzburg-Landau equation in a population problem and an elliptic equation with a harmonic potential are considered. Related spectral schemes are proposed, and their convergence is proved. Numerical results demonstrate the spectral accuracy of this approach.

CDO模型的市场重构与LDG分布
徐承龙,徐晓芸
同济大学学报, 38(2010), 1496-1500.
摘要
在违约损失率(LGD)是随机变量的假设下,应用推广的两因子高斯-Copula CDO定价框架,通过极小化相对墒,讨论了利用市场公开报价数据进行系统违约因子和LGD分布的重构问题。计算结果验证了违约具有偏态性的特点。因此我们的模型可看成是对高斯-Copula模型的一个修正。在计算该问题时,我们采用了迭代方法,避免了处理非线性问题以及非光滑优化问题的求解困难。数值计算结果表明算法是稳定和收敛的。

 -optimal designs for a hierarchically ordered system of regression models
Rongxian Yue and Xin Liu
Comp. Stat. Data Anal., 54(2010), 3458–3465.
Abstract
 -optimal designs are described for a kind of hierarchically ordered system of regression models with an r-dimensional response variable y. The components of y may be correlated with a known variance_covariance matrix  . The present results show that  –optimal designs for this system of regression models do not depend on  . The   –optimal designs are given for the systems of trigonometric and Haar wavelet regression models, respectively.

Bayesian robust designs for linear models with possible bias and correlated errors
Rongxian Yue and Xiaodong Zhou
Metrika 71 (2010), 1–15.
Abstract
Consider the design problem for the approximately linear model with serially correlated errors. The correlated structure is the qth degree moving average process, MA(q), especially for q = 1, 2. The optimal design is derived by using Bayesian approach. The Bayesian designs derived with various priors are compared with the classical designs with respect to some specific correlated structures. The results show that any prior knowledge about the sign of the MA(q) process parameters leads to designs that are considerately more efficient than the classical ones based on homoscedastic assumptions.

Robust designs for models with possible bias and correlated errors
Rongxian Yue and Xiaodong Zhou
Appl. Math. J. Chin. Univ., 25(2010), 307-317.
Abstract
This paper studies the model-robust design problem for general models with an unknown bias or contamination and the correlated errors. The true response function is assumed to be from a reproducing kernel Hilbert space and the errors are fitted by the q-th order moving average process MA(q), especially the MA(1) errors and the MA(2) errors. In both situations, design criteria are derived in terms of the average expected quadratic loss for the least squares estimation by using a minimax method. A case is studied and the orthogonality of the criteria is proved for this special response. The robustness of the design criteria is discussed through several numerical examples.



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发布日期: 12/31/2010
浏览次数: 2458

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