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第一届福建省计算数学学术研讨会暨福建省数学建模与高性能科学计算重点实验室2017年会

发布时间:2017年12月15日 浏览次数:发布者:mathky

会议日程安排

主持人:许传炬

09:00-09:25

尤延诚

厦门大学

Numerical Simulation and POD Analysis of Unsteady   Flows in Aerospace Engineering Applications

09:25-09:50

陈竑焘

厦门大学

A recovery based linear finite element method for   4th order problems

09:50-10:15

黄宝华

福建师范大学

Error bounds for tensor   complementarity problems and some classes of structured tensors

10:15-10:35

休息

10:35-11:00

黄灿

厦门大学

A new   convergence analysis of FEM for fractional Fokker-Planck equation with   general forcing

11:00-11:25

李成梁

福建师范大学

On Euler   preconditioned single-step HSS iterative method for a class of complex   symmetric linear systems

11:25-11:50

吕长青

福建师范大学

A   Levenberg-Marquardt method for solving semi-symmetric tensor equations

主持人:邱建贤

14:00-14:25

牛晓花

集美大学

Dislocation   climb models: from atomistic schemes to dislocation dynamics

14:25-14:50

王靖岳

福州大学

各向异性离散TV极小化模型的一些数值分析

14:50-15:15

翁智峰

华侨大学

A   stabilized finite element method for the convection dominated diffusion   optimal control problem

15:15-15:35

休息

15:35-16:00

闫金亮

武夷学院

Some New   Energy-Preserving Finite Volume Element Methods for the Modified Korteweg-de   Vries Equation

16:00-16:25

翟术英

华侨大学

A Fourier   spectral method for fractional- in-space Cahn-Hilliard equation

16:25-16:50

陈焕阳

厦门大学

变换天文学以及完美隐身的若干数学问题

17:00-18:00

重点实验室成员工作会议

办公楼B313会议室

主持人:沈捷

 


学术报告题目与摘要

 

1、报告人:尤延诚 厦门大学

题目:Numerical Simulation and POD Analysis of Unsteady Flows in Aerospace Engineering Applications

 

2、报告人: 陈竑焘 厦门大学

题目:A recovery based linear finite element method for 4th order problems

摘要:We analyze a gradient recovery based linear finite element method to solve string equations and the corresponding eigenvalue problems. Our method uses only $C^0$ element, which avoids complicated construction of $C^1$ elements and nonconforming elements. Optimal error bounds under various Sobolev norms are established. Moreover, after a post-processing the recovered gradient is superconvergent to the exact one. Finally, some numerical experiments are presented to validate our theoretical findings.

 

3、报告人: 黄宝华  福建师范大学

题目:Error bounds for tensor complementarity problems and some classes of structured tensors

摘要:In this talk, we focus on the local bounds for tensor complementarity problems. With respect to R0-tensor, we introduce the quasi-strongly R0-mapping and reformulation equation, and derive two equivalent definitions of R0-tensor. Moreover, we obtain the global error bounds for tensor complementarity problems with a R0-tensor by means of a given local error bound. We prove global upper and lower bounds for the solution of tensor complementarity problems with a P-tensor by means of two quantities. With the help of the smallest H-eigenvalue and Z-eigenvalue of P-tensor, we establish global upper bounds for solution of the tensor complementarity problems with a P-tensor.

 

4、报告人: 黄灿 厦门大学

题目:A new convergence analysis of FEM for fractional Fokker-Planck equation with general forcing

摘要:Two new convergence analyses are given for the finite element spatial discretization and piecewise-constant time discretization scheme that is used in [K. Le et al., SIAM J. Numer. Anal., (54) 2016, pp.1763–1784] to solve the time-fractional Fokker-Planck equation on a domain Ω × [0, T ] with general forcing, i.e., where the forcing term is a function of both space and time. First, when the method is discretised only in space, stability and convergence are proved in a fractional norm that is stronger than the L2(Ω) norm used in the above paper. Furthermore, unlike the bounds proved in Le et al., the constant multipliers in our analysis do not blow up as the order of the fractional derivative α approaches the classical value of 1. Second, when the method is discretised only in time, we present a new L2(Ω) convergence proof that avoids a flaw in the proof of Theorem 4.4 of the Le et al. paper. 

 

 

5、报告人: 李成梁 福建师范大学

题目:On Euler preconditioned single-step HSS iterative method for a class of complex symmetric linear systems

报告摘要:In this talk, we propose an Euler preconditioned single-step HSS (EP*SHSS) iterative method for a class of complex symmetric linear systems. The proposed method can be applied not only to the nonsingular complex symmetric linear systems but also to the singular ones. The convergence conditions for nonsingular complex symmetric linear systems and semi-convergence conditions for singular ones of the EP*SHSS iterative method are derived under suitable restrictions. Moreover, we consider the acceleration of the EP*SHSS iterative method by Krylov subspace methods and discuss the spectral properties of the corresponding preconditioned matrix. Numerical experiments verify the effectiveness and robustness of the EP*SHSS iterative method either as a solver or a preconditioner for GMRES for solving both nonsingular and singular complex symmetric linear systems.

 

6、报告人: 吕长青 福建师范大学

题目:A Levenberg-Marquardt method for solving semi-symmetric tensor equations

摘要:In this talk, we propose a Levenberg-Marquardt (LM) method for solving tensor  equations with semi-symmetric coefficient tensor and prove its global convergence and local quadratic convergence under the local error bound condition, which is weaker than non-singularity. As application, we solve H-eigenvalue of real semi-symmetric tensor by the LM method. At last, some numerical examples are provided to illustrate the efficiency and validity of these methods proposed.

 

7、报告人: 牛晓花 集美大学

题目:Dislocation climb models: from atomistic schemes to dislocation dynamics

摘要:Dislocation climb mechanism plays an important role in the plastic deformation of crystal materials at high temperature. In this talk, I present a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscaling from a stochastic model on the atomistic scale. This models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. This mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. This climb velocity formula is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Simulations performed show evolution, translation, coalescence of prismatic loops and the interaction between a prismatic loop and an infinite edge dislocation are in excellent  agreement with available experimental and atomistic results.

 

8、报告人: 王靖岳 福州大学

题目:各向异性离散TV极小化模型的一些数值分析

摘要:Functions with bounded total variation (TV) are widely seen in problems dealing with free discontinuities, such as image processing, mean curvature flows, front tracking, and others. We are concerned with the relationship between isotropic and anisotropic discrete total variation operators specifically used in the Rudin-Osher-Fatemi image denoising model. Isotropic TV operators yields boundary shapes that tend to be circles, while anisotropic TV prefers shapes that are compatible with the Wulff shape associated with its anisotropic function. It has been found that minimization problems utilizing a special type of anisotropic TV operator, N-neighbour anisotropic TV, can be computed with a very fast algorithm called graph-cut method. Unfortunately this algorithm can not be used on isotropic TV due to the loss of coarea formula for isotropic discrete TVs. It has also been observed that N-neighbour anisotropic TV minimization yields similar result to isotropic TV minimization as the number of neighbour points increases. We describe the general formula to construct N-neighbour anisotropic TV operators and prove the error between the anisotropic and isotropic TV minimizations. We also do some numerical experiments.

9、报告人: 翁智峰 华侨大学

题目:A stabilized finite element method for the convection dominated diffusion optimal control problem

摘要:In this paper, a stabilized finite element method for optimal control problems governed by a convection dominated diffusion equation is investigated. The state and the adjoint variables are approximated by piecewise linear continuous functions with bubble functions. The control variable either is approximated by piecewise linear functions (called the standard method) or is not discretized directly (called the variational discretization method). The stabilization term only depends on bubble functions, and the projection operator can be replaced by the difference of two local Gauss integrations. A priori error estimates for both methods are given and numerical examples are presented to illustrate the theoretical results.

 

10、报告人: 闫金亮 武夷学院

题目: Some New Energy-Preserving Finite Volume Element Methods for the Modified Korteweg-de Vries Equation

摘要: In this report, some conservative schemes are proposed and compared for the modified Korteweg-de Vries equation, especially with regard to their accuracy and conservative properties. The schemes are constructed using the discrete variational derivative method and the finite volume element methodthe Hamiltonian boundary value method and the Fourier pseudo-spectral method, to inherit the properties of the original equation. Numerical experiments are given to confirm the theoretical results and the capacity of the proposed methods for capturing the solitary wave phenomena.

 

11、报告人: 翟术英 华侨大学

题目: A Fourier spectral method for fractional-in-space Cahn-Hilliard equation

摘要:In this paper, a fractional extension of the Cahn–Hilliard (CH) phase field model is proposed, i.e. the fractional-in-space CH equation. The fractional order controls the thickness and the lifetime of the interface, which is typically diffusive in integer order case. An un- conditionally energy stable Fourier spectral scheme is developed to solve the fractional equation with periodic or Neumann boundary conditions. This method is of spectral accuracy in space and of second-order accuracy in time. The main advantages of this method are that it yields high precision and high efficiency. Moreover, an extra stabilizing term is added to obey the energy decay property while maintaining accuracy and simplicity. Numerical experiments are presented to confirm the accuracy and effectiveness of the proposed method.

 

12、报告人: 陈焕阳 厦门大学

题目:变换天文学以及完美隐身的若干数学问题

摘要:在这个报告里,我将简单汇报天文学和变换光学的交叉,并通过三个例子:类宇宙弦的拓扑、类闵氏时空双曲材料的PML以及完美隐身的新形式,希望提出一些数学问题,并希望和同事们展开新的合作。


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