Local-in-time adjoint-based method for design optimization of unsteady flows

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations.     

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc.     

基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

A simultaneous approach to inverse source problem by Green's function

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation u_t = u_xx + F(t) and u₀(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Fréchet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Fréchet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

A note on spectrum distribution of constraint preconditioned generalized saddle point matrices

In this note, results concerning the eigenvalue distribution and form of the eigenvectors of the constraint preconditioned generalized saddle point matrix and its minimal polynomial are given. These results extend previous ones that appeared in the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

关于反中心对称矩阵的某些性质探讨

利用反中心对称矩阵的定义以及翻转矩阵等技巧,给出了反中心对称矩阵的伴随矩阵、特征值及特征向量的一些新结论.     

Binding energy of an off-center donor impurity in ellipsoidal quantum dot with parabolic confinement potential

The binding energy of an off-center hydrogenic donor impurity in weakly oblate Ellipsoidal Quantum Dot (EQD), using the expansion method within the framework of effective mass approximation in strong confinement, is investigated. In this regard, the binding energies of different states of GaAs structures, as functions of the donor position and ellipticity parameter, are calculated. The results show that variations of binding energies are proportional to the ellipticity constant, the dot dimension and the location of impurity.