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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 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

ON DISCRETE PROJECTION AND NUMERICAL BOUNDARY CONDITIONS FOR THE NUMERICAL SOLUTION OF THE UNSTEADY INCOMPRESSIBLE NAVIER-STOKESEQUATIONS

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Journal of Computational Mathematics 2002年第1期20卷 35-56页

作者： Lan Chieh Huang (ICMSEC, academy of Mathematics and System sciences, chinese academy of sciences, beijing 100080, china) ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences 北京 100080

Focuses on a study on the fully implicit Crank Nicholson (CN) schemes and three projection methods for approximate preservation of component-consistency under projection. Transformation from incompressible Navier-Stokes equations to differential algebraic equations CN schemes; Local errors of CN projection methods; Numerical boundary conditions.

关键词： differential algebraic equations discrete projection numerical boundary conditions

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 sciences, 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

Transformations and non-degenerate maps

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Science china Mathematics 2005年第z1期48卷 195-205页

作者： LI Baokui & WANG Yuefei Institute of Mathematics, academy of Mathematics and System sciences, chinese academy of sciences, beijing 100080, china Graduate School, chinese academy of sciences, beijing 100080, china Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Graduate School Chinese Academy of Sciences Beijing China

We shall prove the equivalences of a non-degenerate circle-preserving map and a M(o)bius transformation in ^Rn, of a non-degenerate geodesic-preserving map and an isometry in Hn of a non-degenerate line-preserving map and an affine transformation in Rn. That a map is non-degenerate means that the image of the whole space under the map is not a circle, or geodesic or line respectively. These results hold without either injective or surjective, or even continuous assumptions, which are new and of a fundamental nature in geometry.

关键词： M(o)bius transformation, circle-preserving map, non-degenerate map.

A CLASS OF NEW PARALLEL HYBRID ALGEBRAIC MULTILEVEL ITERATIONS

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Journal of Computational Mathematics 2001年第6期19卷 651-672页

作者： Zhong-zhi Bai (LSEC ICMSEC, academy of Mathematics and Systems sciences, chinese academy of sciences, beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents preconditioning matrices having parallel computing function for the coefficient matrix and a class of parallel hybrid algebraic multilevel iteration methods for solving linear equations. Solution to elliptic ... 详细信息

关键词： elliptic boundary value problem system of linear equations symmetric positive definite matrix multilevel iteration parallel method

COMPOSITE-STEP LIKE FILTER METHODS FOR EQUALITY CONSTRAINT PROBLEMS

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Journal of Computational Mathematics 2003年第5期21卷 613-624页

作者： Pu-yan Nie(LSEC, ICMSEC, academy of Mathematics and System sciences, chinese academy of sciences, beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

In a composite-step approach, a step Sk is computed as the sum of two components Uk and hk. The normal component Vk, which is called the vertical step, aims to improve the linearized feasibility, while the tangential component hk, which is also called horizontal step, concentrates on reducing a model of the merit functions. As a filter method, it reduces both the infeasibility and the objective function. This is the same property of these two methods. In this paper, one concerns the composite-step like filter approach. That is, a step is tangential component hk if the infeasibility is reduced. Or else, Sk is a composite step composed of normal component Uk, and tangential component hk.

关键词： Composite-step like approaches Filter methods Equality constraints Sequen- tial quadratic programming(SQP) algorithms Normal component Tangential component Convergence.

THE DUAL MIXED METHOD FOR AN UNILATERAL PROBLEM

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Journal of Computational Mathematics 2003年第6期21卷 733-746页

作者： Lie-heng Wang(LSEC, ICMSEC, academy of Mathematics and System sciences, chinese academy of sciences,beijing 100080, china) LSEC ICMSEC Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China

In this paper, the dual mixed method for an unilateral problem, which is the simplified modelling of scalar function for the friction-free contact problem, is considered. The dual mixed problem is introduced, the existence and uniqeness of the solution of the problem are presented, and error bounds O(h3/4) and O(h3/2) are obtained for the dual mixed finite element approximations of Raviart-Thomas elements for k = 0 and k = 1 respectively.

关键词： Dual Mixed Method Unilateral Problem.

CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS

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Journal of Computational Mathematics 2001年第5期19卷 539-548页

作者： Yu-hong Dai (LSEC, ICMSEC, academy of Mathematics and Systems sciences, chinese academy of sciences,beijing 100080, china) 中科院计算数学与科学工程计算所北京 100080

Presents a study on methods for unconstrained optimization. Assumptions of the study; Main results; Convergence properties of the methods under simplified Armijo-type line search.

关键词： unconstrained optimization conjugate gradient (generalized) line search global convergence

SYMPLECTIC COMPUTATION OF HAMILTONIAN SYSTEMS (I)

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Journal of Computational Mathematics 2002年第3期20卷 267-276页

作者： Yi-fa Tang(LSEC,ICMSEC,academy of Mathematics and System sciences, chinese academy of sciences,beijing 100080, china) 中科院数学与系统科学院 LSEC ICMSEC CAS 北京 100080

Presents information on a study which discussed a symplectic computation of hamiltonian systems. Terms of formal energy of mid-point rule; Analysis of the mathematical pendulum to test the convergence of the formal en... 详细信息

关键词： mid-point rule formal energy