会议主题报告

时间

报告人

报告题目

主持人

8:30-

9:30

Lin Mu

University   of Georgia

Pressure Robust Scheme   for Incompressible Flow

葛志昊

9:30-

10:30

Haibiao Zheng

(郑海标)

华东师范大学

An ensemble algorithm   for a parabolic two domain problem

10:30-11:30

Yueqiang Shang

(尚月强)

西南大学

A new   two-level defect-correction method for the steady Navier–Stokes equations

报告题目

Pressure Robust Scheme for   Incompressible Flow

摘要

In this talk, we shall introduce   the recent development regarding the pressure robust weak Galerkin finite   element method (FEM) for solving incompressible flow. Weak Galerkin (WG)   Method is a natural extension of the classical Galerkin finite element method   with advantages in many aspects. For example, due to its high structural   flexibility, the weak Galerkin finite element method is well suited to most   partial differential equations on the general meshing by providing the needed   stability and accuracy. In this talk, the speaker shall discuss the new   divergence preserving schemes in designing the robust numerical schemes. Due   to the viscosity and pressure independence in the velocity approximation, our   scheme is robust with small viscosity and/or large permeability, which   tackles the crucial computational challenges in fluid simulation. We shall   discuss the details in the implementation and theoretical analysis. Several   numerical experiments will be tested to validate the theoretical conclusion.

报告人简介

Dr. Lin Mu is currently an   assistant professor at Department of Mathematics, University of Georgia.   Before moving to UGA, she was a householder fellow working at ORNL. Dr. Mu   received her Ph.D. in Applied Science from the University of Arkansas in 2012   and her M.Sc. and B.S in Computational Mathematics from Xi'an Jiaotong   University in 2009 and 2006. Dr. Mu's areas of interest include: Applied   Mathematics, Numerical Analysis and Scientific Computing; Theory and   Application of Finite Element Methods, Adaptive Methods, Post-processing   approach; Multiscale Modeling approach and Efficient Numerical Solver to   engineering, chemistry, biology and material sciences.

报告题目

An ensemble algorithm for a   parabolic two domain problem

摘要

We propose and analyze an   efficient ensemble algorithm for a parabolic two domain problem. This report   considers a simplified model-two heat equations-in adjoined by an interface.   This algorithm employs the same coefficient matrix for all ensemble members at   each time step, reducing the problem of solving multiple linear system to   solving one linear system with multiple right-hand sides. Moreover, it   decouples the couple system into two subdomain problems, which reduces the   size of the linear systems and allows parallel computation of the two   subdomain problems. One part of interface term is lagged and another part   based on passing interface values back and forth across . Stability and   convergence results are derived. Numerical experiments are presented to support   the theoretical results.

报告人简介

郑海标，华东师范大学副教授，博士生导师。2012年至2014年在西安交通大学工作。2014年至今在华东师范大学工作。目前主要研究方向为不可压缩流动问题、多区域多物理问题的建模、模拟与相关数值算法。在SIAM Journal on   Numerical Analysis, SIAM Journal on Scientific Computing，Computer   Methods in Applied Mechanics and Engineering等期刊上发表学术论文多篇。曾获陕西省科学技术奖二等奖（第二完成人）和陕西省优秀博士论文等奖励。曾在英国剑桥大学、美国匹兹堡大学、香港城市大学等多个大学交流访问

报告题目

A new two-level   defect-correction method for the steady Navier–Stokes equations

摘要

In this talk, I   will present a new defect-correction method based on subgrid stabilization   for the simulation of steady incompressible Navier-Stokes equations with high   Reynolds numbers. The method uses a two-grid finite element discretization   strategy and consists of three steps: in the first step, a small nonlinear   coarse mesh system is solved, and then, in the following two steps, two   Newton-linearized fine mesh problems which have the same stiffness matrices   with only different right-hand sides are solved. The nonlinear coarse mesh system   incorporates an artificial viscosity term into the Navier-Stokes system as a   stabilizing factor, making the nonlinear system easier to resolve. While the   linear fine mesh problems are stabilized by a subgrid model defined by an elliptic   projection into lower-order finite element spaces for the velocity. Error   bounds of the approximate solutions are estimated. Algorithmic parameter   scalings are derived from the analysis. Effectiveness of the proposed method   is also illustrated by some numerical results.

报告人简介

尚月强，1976年12月生，西南大学数学与统计学院教授，博士生导师。2009年12月毕业于西安交通大学计算数学专业，获理学博士学位；2010年10月年至2011年10月在韩国仁荷大学做博士后研究，先后受邀到瑞典于默奥大学、林奈大学、瑞典国家高性能计算中心访学。2012年被破格评为教授，2015年被评为博士生导师。主要从事偏微分方程数值解、计算流体力学和并行计算方面的研究，研究兴趣包括流体力学中的高效（并行）数值方法，并行数值代数，有限元方法，两重网格方法，区域分解算法等。主持国家自然科学基金、教育部留学回国人员基金、省部级科研基金等项目共10余项，在在《J. Comput. Phys.》《Comput. Methods Appl. Mech. Engrg.》《J.   Sci. Comput.》《中国科学：数学》等国内外期刊发表学术论文80余篇，其中SCI收录50余篇。