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ON THE CENTRAL RElaXING SCHEMES I:SINGLE CONSERVATION laWS

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Journal of computational Mathematics 2000年第3期18卷 313-324页

作者： Hua-zhong Tang (LSEC, Institute of computational Mathematics and Scientific /Engineering Computing, academy of Mathematics and System {2., chinese academy of {2., beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents a central relaxing scheme for scalar conservation laws. Details on the preliminary equations; Properties of the relaxed schemes; Conclusions.

关键词： hyperbolic conservation laws the relaxing scheme TVD cell entropy inequality

THE L^2.NORM ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT METHOD FOR THE 2.D ORDER ELLIPTIC PROBLEM WITH THE LOWEST REGUlaRITY

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Journal of computational Mathematics 2000年第3期18卷 277-282页

作者： Lie-heng Wang (LSEC, Institute of computational Mathematics and Scientific/Engineering Computing, academy of Mathematics and System {2., chinese academy of {2., beijing, 100080, china) 中科院计算数学与科学工程计算所科学与工程计算国家重点实验室北京 100080

Presents the abstract L...-norm error estimate of nonconforming finite element method. Use of the Aubin Nitsche Lemma in estimating nonconforming finite element methods; Details on the equations.

关键词： L-2.norm error estimate nonconforming f.e.m. lowest regularity

Application of asymptotic waveform approximation technique to hybrid FE/BI method for 3D scattering

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Science in china(Series F) 2007年第1期50卷 124-134页

作者： PENG Zhen1,2.3 & SHENG XinQing2.1 Institute of Electronics, chinese academy of {2., beijing 100080, china 2.Department of Electronic Engineering, beijing Institute of Technology, beijing 100081, china 3 graduated University of chinese academy of {2., beijing 100039, china 1. Institute of Electronics Chinese Academy of Sciences Beijing 100080 China 2. Department of Electronic Engineering Beijing Institute of Technology Beijing 100081 China 3. graduated University of chinese {2. of sciences Beijing 100039 China

The asymptotic waveform evaluation （AWE） technique is a rational function approximation method in computational mathemetics, which is used in many appllcations in computational electromagnetlca. In this paper, the performance of the AWE technique in conjunction with hybrid finite element/boundary integral （FE/BI） method is firstly Inveetlgeted. The formuletlon of the AWE applied in hybrid FE/BI method is given in detail. The characteristic implementation of the application of the AWE to the hybrid FE/BI method is discussed. Numarlcel results demonstrate that the AWE technique can greatly speed up the hybrid FE/BI method to acquire wide-band and wide-angle backecatter radar-cross-section （RCS） by complex targets.

关键词： hybrid FE/BI AWE electromagnetic scattering RCS

UNCONSTRAINED METHODS F0R GENERALIZED NONLINEAR COMPLEMENTARITY AND VARIATIONAL INEQUALITY PROBLEMS

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Journal of computational Mathematics 1996年第2期14卷 99-107页

作者： J.M. Peng(LSEC Institute of computational Mathematics and Scientific/Engineering Cmputing,chinese {2. of sciences, beijing, china) 中科院计算数学与科学工程计算所北京

In this papert we construct unconstrained methods for the generalized nonlinearcomplementarity problem and variational inequalities. Properties of the correspon-dent unconstrained optimization problem are studied. We apply these methods tothe subproblems in trust region method, and study their interrelationships. Nu-merical results are also presented.

关键词： Math UNCONSTRAINED METHODS F0R GENERALIZED NONLINEAR COMPLEMENTARITY AND VARIATIONAL INEQUALITY PROBLEMS

Direct Optimization of Low-thrust Many-revolution Earth-orbit Transfers

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chinese Journal of Aeronautics 2009年第4期22卷 426-433页

作者： Gao Yang academy of Opto-Electronics,chinese academy of sciences,beijing 100190,china [a]academy of Opto-Electronics Chinese Academy of Sciences Beijing 100190 China

Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.

关键词： low thrust orbital transfer optimization direct method orbital averaging Lyapunov method

Convergence analysis of the adaptive finite element method with the red-green refinement

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Science china Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2.? & SHI ZhongCi 1 1 State Key laboratory of Scientific and Engineering Computing, Institute of computational Mathematics and Scientific/Engineering Computing, {2. of Mathematics and Systems Science, chinese {2. of sciences, beijing 100190, china 2.Key laboratory of Mathematics and Applied Mathematics (Peking University), Ministry of Education and School of Mathematical sciences, Peking University, beijing 100871, china 3 {{12. University of chinese {2. of sciences, beijing 100190, china 1. State Key laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

A computational model for feature binding

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Science china(Life sciences) 2008年第5期51卷 470-478页

作者： SHI ZhiWei1,2. SHI ZhongZhi1, LIU Xi1,2.& SHI ZhiPing1 1 Key laboratory of Intelligent Information Processing, Institute of Computing Technology, chinese {2. of sciences, beijing 100190, china 2.graduate University of chinese {2. of sciences, beijing 100049, china Key laboratory of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences Beijing 100190 China graduate University of chinese {2. of sciences Beijing 100049 China

The "Binding Problem" is an important problem across many disciplines, including psychology, neuroscience, computational modeling, and even philosophy. In this work, we proposed a novel computational model, Bayesian Linking Field Model, for feature binding in visual perception, by combining the idea of noisy neuron model, Bayesian method, Linking Field Network and competitive mechanism. Simulation Experiments demonstrated that our model perfectly fulfilled the task of feature binding in visual perception and provided us some enlightening idea for future research.

关键词： Binding Problem computational model Bayesian Linking Field Model

NUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESHNUMERICAL SOLUTION OF THE UNSTEADYINCOMPRESSIBLE NAVIER-STOKES EQUATIONS ON THECURVILINEAR HALF-STAGGERED MESH

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Journal of computational Mathematics 2000年第5期18卷 521-540页

作者： lan-chieh Huang (Institute of computational Mathematics and Scientific/Engineering Computing, chinese {2. of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

In this paper, the Crank-Nicholson + component-consistent pressure correction method for the numerical solution of the unsteady incompressible Navier-Stokes equation of [1] on the rectangular half-Staggered mesh has been extended to the curvilinear half-Staggered mesh. The discrete projection, both for the projection step in the solution procedure and for the related differential-algebraic equations, has been carefully studied and verified. It is proved that the proposed method is also unconditionally (in t) nonlinearly stable on the curvilinear mesh, provided the mesh is not too skewed. It is seen that for problems with an outflow boundary, the half-Staggered mesh is especially advantageous. Results of preliminary numerical experiments support these claims.

关键词： Unsteady incompressible Navier-Stokes equations Curvilinear half- staggered mesh Discrete projection.

Subspace Search Method for Quadratic Programming With BoxConstraints

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Journal of computational Mathematics 1999年第3期17卷 307-314页

作者： Zi-luan Wei(ICMSEC, chinese academy of {2., beijing 100080, china) 中科院计算数学与科学工程计算所北京

A subspace search method for solving quadratic programming with box constraints is presented in this paper. The original problem is divided into many independent subproblem at an initial point, and a search direction is obtained by solving each of the subproblem, as well as a new iterative point is determined such that the value of objective function is decreasing. The convergence of the algorithm is proved under certain assumptions, and the numerical results are also given.

关键词： subspace search method quadratic programing matrix splitting