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THE LARGE TIME CONVERGENCE OF SPECTRAL METHOD FOR GENERALIZED KURAMOTO-SIVASHINSKY EQUATION (Ⅱ)

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Journal of Computational Mathematics 1998年第3期16卷 203-212页

作者： Xin-ming Xiang (shanghai Normal university, shanghai 200234, china) 上海师范大学上海

In this paper, we study fully discrete spectral method and long time behavior of solution of generalized Kuramoto-Sivashinsky equation with periodic initial condition. We prove that the large time error estimation for fully discrete solution of spectral method. We prove the existence of approximate attractors AN, ANk respectively and d(AN, A) → 0, d(ANk, A) → 0.

关键词： Kuramoto- Sivashinsky equation,large time convergence Approximate attractor Upper semicontinuity of attractors.

EMMA:An Efficient Massive Mapping Algorithm Using Improved Approximate Mapping Filtering

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Acta Biochimica et Biophysica Sinica 2006年第12期38卷 857-864页

作者： Xin ZHANG~1 Zhi-Wei CAO~2 Zhi-Xin LIN~3 Qing-Kang WANG~1* Yi-Xue LI~4 1 Institute of Micro/Nano Science and Technology,shanghai Jiaotong university,shanghai 200030,china 2 shanghai Center for Bioinformation Technology,shanghai 200235,china 3 College of Life Science and Technology,shanghai Jiaotong university,shanghai 200030,china 4 Bioinformation Center of shanghai Institutes for Biological Sciences,Chinese Academy of Sciences,shanghai 200031,china Institute of Micro/Nano Science and Technology Shanghai Jiaotong UniversityShanghai 200030 China shanghai Center for Bioinformation Technology Shanghai 200235 China College of Life Science and Technology Shanghai Jiaotong UniversityShanghai 200030 China Bioinformation Center of shanghai Institutes for Biological Sciences Chinese Academy of SciencesShanghai 200031 China

Efficient massive mapping algorithm (EMMA),an algorithm on efficiently mapping massivecDNAs onto genomic sequences,has recently been *** process of mapping massive cDNAsonto genomic sequences has been improved using more approximate mapping filtering based on an enhancedsuffix array coupled with a pruned fast hash table,algorithms of block alignment extensions,and *** compared with the classical BLAT software in this field,the computing of EMMA ranges fromtwo to forty-one times faster under similar prediction precisions.

关键词： cDNA mapping maximal exact match enhanced suffix array pruned fast hash table extension algorithm

Virtual multi-dimensional internal bonds model and its application in simulation of rock mass

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Science china(Technological Sciences) 2008年第2期51卷 192-201页

作者： ZHANG ZhenNan1,2 & GE XiuRun3,4 1 Department of Civil Engineering,shanghai university,shanghai 200072,china 2 shanghai Institute of Applied Mathematics and Mechanics,shanghai university,shanghai 200072, china 3 Institute of Geotechnical Engineering,shanghai Jiao Tong university,shanghai 200030,china 4 Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan 430071,china Department of Civil Engineering Shanghai University Shanghai China shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China Institute of Geotechnical Engineering Shanghai Jiao Tong University Shanghai China Institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan China

VMIB (virtual multi-dimensional internal bonds) is a multiscale mechanical model developed from the VIB (virtual internal bond) theory. In VIB theory,the solid mate-rial is considered to consist of random-distributed material particles in microscale. These particles are connected with normal bonds. The macro constitutive relation is derived from the cohesive law between particles. However,in VMIB,the micro particles are connected with both normal and shear bonds. The macro constitutive relation is derived in terms of bond stiffness coefficients. It has been theoretically certified that there exists a corresponding relationship between the two bond stiffness coefficients and the two macro material constants,i.e. the Young’s modulus and Poisson ratio. This corresponding relationship suggests that it should be necessary and sufficient to simultaneously account for the normal and shear interactions between particles. Due to the fact that the fracture criterion is directly incorporated into the constitutive relation,both VIB and VMIB present many advantages in simulating fractures of materials. In the damage model of rock mass,a damage tensor is usually defined to describe the distribution of cracks. The damage value in one direction determines the relative stiffness of rock mass in this direction. In VMIB solid,the relative distribution density of micro bonds in one direction determines the relative macro stiffness of the material in this direction. The effects of the damage value and the relative distribution density of bonds are consistent. To simulate the failure behavior of rock mass with VMIB,the presented paper sets up a quantitative relationship between the damage tensor and the rela-tive distribution density of bonds. Comparison of the theoretical and the experi-mental results shows that VMIB model can represent the effect of distributed cracks on rock mass with this relationship. The presented work provides a founda-tion for further simulating fracture behavior

关键词： VMIB (virtual multi-dimensional internal bonds) rock mass VIB (virtual internal bonds) multi-cracked body numerical simulation

An extended stochastic response surface method for random field problems

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Acta Mechanica Sinica 2007年第4期23卷 445-450页

作者： Shuping Huang Xinjian Kou shanghai Jiaotong university,shanghai 200240,china shanghai Jiaotong university Shanghai China

An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method （SRSM） which has been previously proposed for problems dealing with random variables only. This paper extends SRSM to problems involving random fields or random processes fields. The favorable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.

关键词： Stochastic response surface Karhunen-Loeve expansion Polynomial chaos Random field Stochastic finite elements

A MONOTONE COMPACT IMPLICIT SCHEME FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2008年第2期26卷 123-148页

作者： Yuanming Wang Department of Mathematics,East china Normal university,shanghai 200241,china Division of Computational Science,E-Institute of shanghai Universities,shanghai Normal Benyu Guo Department of Mathematics,shanghai Normal university,shanghai 200234,china Division of Computational Science,E-Institute of shanghai Universities,shanghai,china Department of Mathematics East China Normal University ShangHai Department of Mathematics Shanghai Normal University ShangHai

A monotone compact implicit finite difference scheme with fourth-order accuracy in space and second-order in time is proposed for solving nonlinear reaction-diffusion equations. An accelerated monotone iterative method for the resulting discrete problem is presented. The sequence of iteration converges monotonically to the unique solution of the discrete problem, and the convergence rate is either quadratic or nearly quadratic, depending on the property of the nonlinear reaction. The numerical results illustrate the high accuracy of the proposed scheme and the rapid convergence rate *** iteration.

关键词： Nonlinear reaction-diffusion equation Monotone compact implicit scheme High accuracy Monotone iteration Rapid convergence rate.

Explicit Analytical Solutions for the Shearingand Radial Stresses in Curved Beams

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Communications in Nonlinear Science and Numerical Simulation 1999年第2期4卷 151-156页

作者： Aiming YU+ Xiangrong LI+++ (Tongji university, shanghai 200092, china)++ (shanghai university, shanghai 200072, china) Tongji university Shanghai 200092 China shanghai university Shanghai 200072 China

The shearing stresses in curved beams can be solved explicitly from anintegral equation, which is obtained by differentiation & integral manipulations. Twonovel formulae for shearing & radial stresses are also presented in the paper. The resultsof an example reveal that the shearing & radial stresses arrive at their maximum valuesslightly below the centroid of the section.

关键词： curved beam shearing stress radial stress integral equation

CURVILINEAR PATHS AND TRUST REGION METHODS WITH NONMONOTONIC BACK TRACKING TECHNIQUE FOR UNCONSTRAINED OPTIMIZATION

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Journal of Computational Mathematics 2001年第3期19卷 241-258页

作者： De-tong Zhu (Department of Mathematics, shanghai Normal university, shanghai 200234, china) 上海师范大学上海 200234

Focuses on a study which examined the modification of type approximate trust region methods via two curvilinear paths for unconstrained optimization. Properties of the curvilinear paths; Description of a method which combines line search technique with an approximate trust region algorithm; Information on the convergence analysis; Details on the numerical experiments.

关键词： curvilinear paths trust region methods nonmonotonic technique unconstrained optimization

DISSIPATIVITY AND EXPONENTIAL STABILITY OF θ-METHODS FOR SINGULARLY PERTURBED DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED LAG

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Journal of Computational Mathematics 2003年第6期21卷 715-726页

作者： Hong-jiong Tian (Department of Mathematics, shanghai Normal university, shanghai 200234, china) department of Mathematics Shanghai Normal University 上海 200234

This paper deals with analytic and numerical dissipativity and exponential stability of singularly perturbed delay differential equations with any bounded state-independent lag. Sufficient conditions will be presented to ensure that any solution of the singularly perturbed delay differential equations (DDEs) with a bounded lag is dissipative and exponentially stable uniformly for sufficiently small ε > 0. We will study the numerical solution defined by the linear θ-method and one-leg method and show that they are dissipative and exponentially stable uniformly for sufficiently small ε > 0 if and only if θ = 1.

关键词： Singular perturbation θ-methods Dissipativity Exponential stability.

A MODIFIED LEVENBERG-MARQUARDT ALGORITHM FOR SINGULAR SYSTEM OF NONLINEAR EQUATIONS

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Journal of Computational Mathematics 2003年第5期21卷 625-636页

作者： Jin-yan Fan (Department of Mathematics, shanghai Jiaotong university, shanghai 200240, china) Department of Mathematics Shanghai Jiaotong University 上海 200240

Based on the work of paper [1], we propose a modified Levenberg-Marquardt algoithm for solving singular system of nonlinear equations F(x) = 0, where F(x) : Rn - Rn is continuously differentiable and F'(x) is Lipschitz continuous. The algorithm is equivalent to a trust region algorithm in some sense, and the global convergence result is given. The sequence generated by the algorithm converges to the solution quadratically, if ||F(x)||2 provides a local error bound for the system of nonlinear equations. Numerical results show that the algorithm performs well.

关键词： Singular nonlinear equations Levenberg-Marquardt method Trust region al- gorithm Quadratic convergence.