Center of Computational and Applied Mathematics

复旦大学-厦门大学计算数学学术研讨会

Kohn-Sham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. 248-272]. This is
consists of a discrete Fourier transform-based 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 high-dimensional 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 co-existent fluid temperature on the motions of droplets are investigated. Our simulation results are in semi-quantitative 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 Active-set 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.

Non-tensor-product 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 genus-0 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 B-spline (DCB-spline), a new non-tensor-product 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 knot-insertion strategies guided by surface geometry and fitting error. Within our framework, a genus-0 model can be converted to a single spherical spline representation whose root mean square error is tightly bounded within a user-specified 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 non-isothermal nucleation and growth processes 

陆帅 (复旦大学) 

Abstract: We study non-isothermal 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 fully-discrete numerical scheme. Finally, we apply these results to the eddy current approximation
of Maxwell's equations.