Moving mesh methods for Boussinesq equation

The Boussinesq equation is a challenging problem both analytically and numerically. Owing to the complex dynamic development of small scales and the rapid loss of solution regularity, the Boussinesq equation pushes any numerical strategy to the limit. With uniform meshes, the amount of computational time is too large to enable us to obtain useful numerical approximations. Therefore, developing effective and robust moving mesh methods for these problems becomes necessary. In this work, we develop an efficient moving mesh algorithm for solving the two‐dimensional Boussinesq equation. Our moving mesh algorithm is an extension of Tang and Tang (SIAM J. Numer. Anal. 2003; 41 :487–515) for hyperbolic conservation laws and Zhang and Tang (Commun. Pure Appl. Anal. 2002; 1 :57–73) for convection‐dominated equations. Several numerical fluxes (Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (2nd edn). Springer: Berlin, 1999; WASCOM 99”: 10th Conference on Waves and Stability in Continuous Media, Porto Ercole, Italy, 1999; 257–264; High‐order Methods for Computational Physics. Springer: Berlin, 1999; 439–582; J. Sci. Comput. 1990; 5 :127–149; SIAM J. Numer. Anal. 2003; 41 :487–515; Commun. Pure Appl. Anal. 2002; 1 :57–73) are also discussed. Numerical results demonstrate the advantage of our moving mesh method in resolving the small structures. Copyright © 2009 John Wiley & Sons, Ltd.     

精细时程积分法及其数值衍生格式应用评估

旋翼气动弹性耦合动力学方程本质上是一组刚性比较大的非线性偏微分方程。在有限元结构离散后，可改写为非齐次微分方程组，其中非齐次项是桨叶运动量（位移与速度）和气动载荷的函数。针对这类方程，本文尝试引入精细积分法及其衍生格式，借助数值方法计算Duhamel积分项。从积分精度与数值稳定性方面比较研究具有代表性的精细库塔法和高精度直接积分法。结合隐式积分算法，评估精细积分法应用于旋翼动力学方程的可行性。算例表明，精细积分法对矩形直桨叶动力学方程具有足够的求解精度。     

二阶常微初值问题的单步格式

讨论二阶常微分方程初值问题utt+au=f,u(0)=u0，ut(0)=v0 的一种单步格式，采用u及v=ut为未知量，计算简单. 证明了此格式的稳定性及对u，v皆有二阶精度. 此格式可用于双曲问题.     

A new family of high-order compact upwind difference schemes with good spectral resolution

This paper presents a new family of high-order compact upwind difference schemes. Unknowns included in the proposed schemes are not only the values of the function but also those of its first and higher derivatives. Derivative terms in the schemes appear only on the upwind side of the stencil. One can calculate all the first derivatives exactly as one solves explicit schemes when the boundary conditions of the problem are non-periodic. When the proposed schemes are applied to periodic problems, only periodic bi-diagonal matrix inversions or periodic block-bi-diagonal matrix inversions are required. Resolution optimization is used to enhance the spectral representation of the first derivative, and this produces a scheme with the highest spectral accuracy among all known compact schemes. For non-periodic boundary conditions, boundary schemes constructed in virtue of the assistant scheme make the schemes not only possess stability for any selective length scale on every point in the computational domain but also satisfy the principle of optimal resolution. Also, an improved shock-capturing method is developed. Finally, both the effectiveness of the new hybrid method and the accuracy of the proposed schemes are verified by executing four benchmark test cases.     

一类自适应运动网格的ALE方法

从积分形式的二维Lagrange流体力学方程组出发,使用ENO高阶插值多项式,推广了四边形结构网格下的一阶有限体积格式,构造一类结构网格下的高精度有限体积格式.结合有效的守恒重映方法,发展一类高精度的ALE方法,并结合自适应运动网格技术,进行ALE方法的数值模拟,得到预期的效果.     

从高等教育的发展到光学工程类专业研究型人才培养方案再调整的思考

浙江大学信息工程(光电)专业自1952年建立以来,为促进国家经济建设和光学工程学科的发展培养了大量的专业人才。21世纪之初,中国的高等教育进入了大众化阶段,科技的进步和社会的发展对光学工程学科人才的培养呈现出了知识多元化和能力专业化的需求,光电信息工程领域对高端研究型人才的培养要求呼之欲出。从中国高等教育的发展背景出发,分析了光学工程类本科人才培养的变迁和现状,介绍了浙江大学本科层次研究型人才培养的新模式,阐述了浙江大学信息工程(光电)专业的整体调整思路和培养方案。     

Novel optical packet with non-return-to-zero label and duobinary carrier-suppressed return-to-zero payload

A novel packet format with non-return-to-zero (NRZ) label and duobinary carrier-suppressed return-to-zero (DCS-RZ) payload is proposed for optical packet switching networks.NRZ label is followed by DCS-RZ payload with a certain guard time.The spectra of the low-rate NRZ label locate around the optical carrier frequency where some parts of the corresponding spectra of the high-rate DCS-RZ payload have been suppressed due to DCS-RZ modulation.At the switching node,the label or payload extraction can be realized simply through an optical bandpass or notch filter respectively.The feasibility of the scheme is verified by the simulation on the famous photonic design platform designed by Virtual Photonics Inc.(VPI).The effects of optical filter bandwidth on the received signal quality are discussed by analyzing bit error rate(BER)and contrast ratio performances.     

Photon statistics measurement for coherent fields

An efficient scheme for photon statistics measurement is presented based on the Hanbury-Brown-Twiss configuration. We set the sampling time Ts to satisfy the relationship of Ts 〈 Td 〈 Tm, where Td is the dead time of each detector and Tm is the laser pulse repetition period. And each single photon detector cannot detect more than one photon in each pulse. The approach can sufficiently eliminate the influences of the detector＇s dead time on photon statistics. At last, the photon statistics of coherent field is experimentally determined.     

大功率GaN基发光二极管的电流扩展效应及电极结构优化研究

定性分析了GaN基LED的电流扩展效应，发现电流密度和电流横向扩展的有效长度对电流均匀扩展有很大影响.基于此，对GaN基大功率LED提出了优化的电极结构，以减缓电流拥挤效应，降低器件串联电阻.通过用红外热像仪测量器件表面的温度分布，发现具有优化的环形插指电极结构的GaN基大功率LED表面温度分布比较均匀，证明芯片接触处电流扩展均匀，局部电流密度降低，减小了焦耳热的产生，增强了器件的可靠性.     

Convergence of subdivision schemes and smoothness of limit functions

Starting with vector λ=(λ(k))_k∈Z∈?p(Z), the subdivision scheme generates a sequence of vectors by the subdivision operator