更新时间：
2014年复旦大学厦门大学 

计算数学研讨会 

（2014年1月11日，星期六，海韵实验楼105报告厅） 



时间 
报告人 
报告题目 
09:30 10:00 
开幕式 合影 

10:0010:35 
高卫国 
KohnSham密度泛函理论中的特征值问题求解 
10:3511:10 
白正简 
A Fast Alternating Minimization Algorithm for Total Variation Deblurring Without Boundary Artifacts 
11:1011:45 
薛军工 
Probabilistic numerical methods for BSDEs and PDEs 
11:4514:30 
午餐 休息 

13:3014:05 
吴聪敏 
MD simulations for motions of evaporative droplets driven by thermal gradients 
14:0514:40 
杨卫红 
A Filter Activeset Algorithm for the Nearest Correlation Matrix with Factor Structure 
14:4015:15 
曹娟 
Nontensorproduct spline and its application in surface reconstruction 
15:1515:45 
茶歇 

15:4516:20 
陆帅 
Parameter identification in nonisothermal nucleation and growth processes 
16:2016:55 
陈竑焘 
Finite element exterior calculus for parabolic problems and its application 
复旦大学厦门大学计算数学学术研讨会
KohnSham密度泛函理论中的特征值问题求解
高卫国(复旦大学)
A Fast Alternating Minimization Algorithm for Total Variation Deblurring Without Boundary Artifacts
白正简(厦门大学)
Abstract: Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang [SIAM J. Imaging Sci., 1 (2008), pp. 248272]. This is consists of a discrete Fourier transformbased alternating minimization algorithm with periodic boundary conditions and in which two fast Fourier transforms (FFTs) are required per iteration. In this paper, we propose a continuous alternating minimization algorithm for the total variation image debarring problem and establish its convergence. The continuous setting is very useful to have a unifying representation of the algorithm, independently of the discrete approximation of the deconvolution problem, in particular concerning the strategies for dealing with boundary artifacts. A discrete version of our continuous alternating minimization algorithm is obtained following two different strategies: the imposition of appropriate boundary conditions and the enlargement of the domain. The first one is computationally useful in the case of a symmetric blur, while the second one can be efficiently applied for a nonsymmetric blur. Numerical tests show that our algorithm generates higher quality images in comparable running times with respect to the Fast Total Variation deconvolution algorithm.
Probabilistic numerical methods for BSDEs and PDEs
薛军工(复旦大学)
Abstract: In this talk we discuss the backward Euler scheme for BSDEs and the numerical challenges associated with it. We also discuss the probabilistic numerical methods for some highdimensional PDEs
MD simulations for motions of evaporative droplets driven by thermal gradients
吴聪敏 (厦门大学)
Abstract: The driving mechanism of fluid transport at nanoscale is one of the key problems on the design of micro and nanofluidic devices. We performed molecular dynamics(MD) simulations to study the motions of evaporative droplets driven by thermal gradients along nanochannels. The effect of droplet size and the effect of the coexistent fluid temperature on the motions of droplets are investigated. Our simulation results are in semiquantitative agreement with the prediction of the continuum model (Xu and Qian 2012 Phys. Rev. E 85 061603). It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (10nm). We also give a theoretical analysis on the size of the thermal singularity. Both the analysis and MD simulations show that that the droplet mobility decreases with decreasing coexistence temperature.
A Filter Activeset Algorithm for the Nearest Correlation Matrix with Factor Structure
杨卫红 (复旦大学)
摘要: 我们主要利用滤子积极集方法求解具有因子结构的最近相关矩阵问题. 具有因子结构的最近相关矩阵问题在担保债务凭证(Collateralized Debt Obligation，简称CDO)和多元时间序列分析中有着重要的应用,由 Borsdorf, Higham, 和 Raydan 在 SIAM J. Matrix Anal. Appl. 2010 年的一篇论文中提出.在该篇论文中, 三位作者采用了几个经典方法: 比如交替方向法、投影梯度法、子空间信赖域法和 SQP 方法等算法进行计算,并且比较了几个方法的计算效果. 经过计算, 我们发现尽管这个问题的变量比较多, 但是最优解的积极集的元素个数很少.因此提出了针对这个问题的滤子积极集方法. 这样做的好处是: 1. 采用积极集方法可以大幅度减少SQP 子问题的规模. 2. 采用滤子方法和回溯方法决定步长, 这样得到的算法整体收敛, 在一定条件下还是线性收敛的.实际数值实验表明计算速度比已有方法提高很多.
Nontensorproduct spline and its application in surface reconstruction
曹娟 (厦门大学)
Abstract: In this talk, we will introduce a novel surface fitting scheme for automatically reconstructing a genus0 object onto a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration Bspline (DCBspline), a new nontensorproduct spline. In this framework, we efficiently compute Delaunay configuration on sphere by the union of two planar Delaunay configurations. Also, we develop a hierarchical and adaptive method that progressively improves the fitting quality by new knotinsertion strategies guided by surface geometry and fitting error. Within our framework, a genus0 model can be converted to a single spherical spline representation whose root mean square error is tightly bounded within a userspecified tolerance. The reconstructed continuous representation has many attractive properties such as global smoothness and no auxiliary knots. Several experiments demonstrate the efficacy of our new approach for reverse engineering and shape modeling.
Parameter identification in nonisothermal nucleation and growth processes
陆帅 (复旦大学)
Abstract: We study nonisothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
Finite element exterior calculus for parabolic problems and its application
陈竑焘 (厦门大学)
Abstract: In this talk, we consider the extension of the finite element exterior calculus from elliptic problems, in which the Hodge Laplacian is an appropriate model problem, to parabolic problems, for which we take the Hodge heat equation as our model problem. The numerical method we study is a Galerkin method based on a mixed variational formulation and using as subspaces the same spaces of finite element differential forms which are used for elliptic problems. We analyze both the semidiscrete and a fullydiscrete numerical scheme. Finally, we apply these results to the eddy current approximation of Maxwell's equations.