数据与计算科学研讨会

数据与计算科学研讨会

报告题目摘要

2017年6月5日盘锦校区C208-201

On Imaging Models Based on Fractional Order Derivatives Regularizer And Their Fast Algorithms

Ke Chen, University of Liverpool, UK

Abstract: In recent years, high order regularizers such as the total generalised variation, the mean curvature and the Gaussian curvature are increasingly studied and applied, and many improved results over the widely-used total variation model are reported. (1)Here we first introduce the fractional order derivatives and the total fractional-order variation which provides an alternative regularizer and is not yet formally analysed.  We demonstrate that existence and uniqueness properties of the new model can be analysed in a fractional BV space, and, equally, the new model performs as well as the high order regularizers (which do not yet have much theory). (2) In the usual framework, the algorithms of a fractional order model are not fast due to dense matrices involved. Moreover, written in a Bregman framework, the resulting Sylvester equation with Toeplitz coefficients can be solved efficiently by a preconditioned solver. Further ideas based on adaptive integration can also improve the computational efficiency in a dramatic way. (3)  Numerical experiments will be given to illustrate the advantages of the new regulariser for both restoration and registration problems. Joint work with Dr J P Zhang (Liverpool and Xiangtan).

Recent Development about Perturbation Analysis for Conic Optimization Problems

Liwei Zhang, Dalian University of Technology, China

Abstract.This talk first summarizes the works about nonlinear conic optimization problems, especially about strong regularity and isolated calmness for nonlinear programming, second-order conic optimization and semidefinite programming.  After that it is devoted to studying  the robust isolated calmness of the Karush-Kuhn-Tucker (KKT) solution mapping  for a large class of  interesting conic programming problems (including most commonly known  ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that  the KKT solution mapping  is robustly isolated calm   if and only if both the strict Robinson constraint qualification   and the second order sufficient condition  hold. This implies, among others, that at a locally optimal solution  the constraint non-degeneracy and the second order sufficient condition are both needed for  the KKT solution mapping  to have  the  Aubin property.

数据分析中的几何方法

苏志勋，大连理工大学

Fast Image denoising algorithm with different BCs

Yuying Shi, North China Electric Power University, China

Abstract: We considered the L₁ fidelity term, the L₂ fidelity term and the combined L₁ and L₂ fidelity term for denoising models. Some authors used the fast Fourier transform (FFT) algorithm which can only use periodic boundary conditions (BCs). In this paper we combine the augmented Lagrangian method (ALM) and the symmetric Red-Black Gauss-Seidel (SRBGS) method to propose three algorithms that are suitable for different BCs. Experimental results show that the proposed algorithms are effective and the model with the combined L₁ and L₂ fidelity term demonstrates more advantages in efficiency and accuracy than other models with the L₁ fidelity term or the L₂ fidelity term.

2017年6月7日大连主校区研教楼510

The Weak Galerkin Method and Its Applications

Xiu Ye (Lin Mu, Junping Wang), University of Pittsburgh, USA

Abstract: The purpose of this presentation is to introduce basis concepts of the Weak Galerkin (WG) methods and their recent developments including new a posteriori estimators and applications on fluid dynamics. Weak Galerkin finite element methods are general methods for solving partial differential equations. The WG method is a natural extension of the standard Galerkin finite element method for the function with discontinuity since they have the same weak forms only where classical derivatives are substituted by weakly defined derivatives. Therefore, the weak Galerkin methods have the flexibility of employing discontinuous elements and, at the same time, share the simple formulations of continuous finite element methods.

Decoupling the coupled Navier-Stokes and Darcy equations

Xiaoming He, Missouri University of Science and Technolog, USA

Abstract: The Navier-Stokes equation coupled with the Darcy equation through interface conditions has attracted scientists’ attention due to its wide range of applications and significant difficulty in the nonlinearity and interface conditions. This presentation discusses a multi-physics domain decomposition method for decoupling the coupled Navier-Stokes-Darcy system with the Beavers-Joseph interface condition. The wellposedness of this system is first showed by using a branch of singular solutions and the existing theoretical results on the Beavers-Joseph interface condition. Then Robin boundary conditions on the interface are constructed based on the physical interface conditions to decouple the Navier-Stokes and Darcy parts of the system. A parallel iterative domain decomposition method is developed according to these Robin boundary conditions and then analyzed for the convergence. Numerical examples are presented to illustrate the features of this method and verify the theoretical results.

Residual thin liquid films in dewetting system

Lei Chen, Nanchang University, China

Abstract: The residual thin films could be left on smooth substrates after the dewetting of liquids. It is of great significance to the fields of energy, electronics, biology, aerospace, etc. Its evolution is governed by Navier-Stokes and continuity equations. In this talk, the thickness and stability of the residual film will be analyzed through a high order ODE and PDE respectively. A finite difference method will be used to solve the high order nonlinear PDE. The results show that the thickness of residual thin film will increase with the increase of dewetting speed. The stability is influenced by the disjoining pressure and the thickness: rupture to several small holes or approach to a stable flat film. The results proved important guidance for long-standing puzzles about trace liquid after dewetting.

2017年6月7日大连主校区研教楼510

散射与反散射问题的数值计算

马富明，吉林大学

摘要：介绍应用与计算数学中一个有广阔应用背景的研究方向。这些问题来自于众多与高技术相关的科学与工程领域，例如地质与深海探测、隐身技术、工业无损探伤、医学成像等。问题的数学模型多为偏微分方程特殊定解问题及其反问题。本报告将介绍此方向研究的基本状况和我们研究集体在此方向的研究成果。

Nonlinear Preconditioning and its Application in Multicomponent Problems

Lulu Liu, University of Lugano, Switzerland

Abstract: The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier–Stokes equations.