BYR Achieve · 镜像论坛

2014年7月9日(周三)上午8:30-11:30 主楼409 时间主持人报告人题目8:30-9:00 李鹤江雪电磁场问题的建模与计算 9:00-9:30 孙聪 Sum rate maximization algorithms for MIMO relay networks in wireless communications 9:30-10:00 寇彩霞 A Nonlinear Conjugate Gradient Algorithm with An Optimal Property and An Improved Wolfe Line Search 10:00-10:30 休息、自由讨论 10:30-11:00 郭永江江彦若干领域中一些非线性发展方程的解析研究 11:00-11:30 李晓莉 Global Solutions of Liquid Crystal Flows and Full Magnetohydrodynamics 11:30-12:00 李卫明 Hypothesis testing for high-dimensional covariance matrices 报告摘要电磁场问题的建模与计算江雪拟稳态 Maxwell 方程是计算电磁学的重要研究方向，在电气工程和微电子技术领域具有广泛应用，如大型变压器、电机等工程设备中的磁通和铁损模拟，大规模集成电路数值仿真，金属材料缺陷的无损探测，随钻测井等。本报告将介绍大型电力变压器中的三维电磁场涡流问题，根据国内变压器产品研发、设计和制造的现状，鉴于节能环保的极端重要性，需要重点研究变压器中的杂散损耗问题。由于变压器中涡流问题可以包含多连通域，并有非线性、各向异性、退化的系数，所以给数值求解带来很大困难。我们针对模拟变压器结构部件的TEAM基准问题进行一系列的研究，建立了求解多尺度非线性涡流问题的有效数学模型和有限元方法，解决了大型变压器模拟的一个工程难题；编写了大型变压器数值模拟的并行自适应有限元程序，为油箱整结构模拟奠定了基础。 Sumrate maximization algorithms for MIMO relay networks in wireless communications孙聪 Sum rate maximization problem is always ofgreat interests in the field of wireless communications. For MIMO relaynetworks, we propose a new approach to approximate sum rate maximization, andprove it is a lower bound of achievable sum rate. To solve the nonlinearnonconvex optimization problem, we first change the fraction function into anon-fraction function in the objective function, and show that the optimizationproblems share the same stationary points. By applying the alternatingminimization method, we decompose the complex problem into several subproblemsthat are easier handled with. We also propose algorithms to solve the nonconvexsubproblems. Simulation results show that our approach achieves higher sum ratethan the compared approaches. Also, our proposed algorithm is applicable tosolve subproblems of other approaches and save much computing time. A Nonlinear Conjugate Gradient Algorithm with An OptimalProperty and An Improved Wolfe Line Search寇彩霞 We seek theconjugate gradient direction closest to the direction of the scaled memorylessBFGS method and propose a family of conjugate gradient methods forunconstrained optimization. An improved Wolfe line search is also proposed,which can avoid a numerical drawback of the original Wolfe line search andguarantee the global convergence of the conjugate gradient method under mildconditions. To accelerate the algorithm, we introduce adaptive restarts alongnegative gradients based on the extent to which the function approximates somequadratic function during previous iterations. Numerical experiments with theCUTEr collection show that the proposed algorithm is promising. 若干领域中一些非线性发展方程的解析研究江彦在自然科学领域和工程领域等诸多领域中，总是存在着许许多多的非线性现象。为了更好地了解这些非线性现象，人们逐渐地将兴趣转移到研究非线性科学。非线性科学作为一门新兴基础学科，在过去的几十年中得到了迅速的发展，其可以用于研究非线性现象的产生原理以及运动规律等。此外，非线性科学衍生出三大研究分支：孤子、分形和混沌。孤子理论作为其中一个分支也取得了相当大的进展，在许多领域中都相继发现了孤子的存在。例如：流体领域中的水波孤子、非线性光学领域中光孤子以及生物领域中的能量孤子等等。对不同领域内孤子现象的研究，归根结底是对所建立的各种各样非线性发展方程的解析研究。本次报告首先简要介绍了孤子的研究背景；其次介绍非线性发展方程的研究方法，特别介绍了其中两种方法的研究路线；最后以几个具体方程为例，对其进行解析研究，并且基于得到的孤子解模拟和讨论各类孤子现象。 Global Solutions of LiquidCrystal Flows and Full Magnetohydrodynamics李晓莉We use a three-level approximationscheme, entropy method and a weak convergence method, Fourier transformmethods, linearized methods, iteration method, interpolation space theory,maximal regularity, Little-Palay decomposition and compact theory, to study twophysically relevant hydrodynamic systems. More precisely, we prove the globalwell-posedness of strong solutions to the initial-boundary value problem forthe density-dependent incompressible flow of liquid crystals, and the globalexistence of a variational (weak) solution to the full compressibleMagnetohydrodynamic flows. Hypothesis testing for high-dimensionalcovariance matrices李卫明 Thispaper discusses the problem of testing for high-dimensional covariancematrices. Tests for an identity matrix and for the equality of two covariancematrices are considered when the data dimension and the sample size are bothlarge. Most importantly, the dimension can be much larger than the sample size.The proposed test statistics are built upon the Stieltjes transform of thespectral distribution of the sample covariance matrix. We prove that the proposedstatistics are asymptotically chi-square distributed under the null hypotheses,and normally distributed under the alternative hypotheses. Simulation resultsshow that for finite dimension and sample size the proposed tests outperform someexisting methods in various cases. 理学院 2014年7月7日 http://portal.bupt.edu.cn//html/main/col38/2014-07/07/20140707160400565586872_1.html

理学院“青年学术论坛”第15期——数学系青年教师学术报告会