12月20日学术报告 （三个）

发布时间:2013-12-17

1. 题 目：A Distributional Monte Carlo Method for the Boltzmann Equation

报告人：Aihua Wood, Professor
(Dept of Mathematics and Statistics, Air Force Institute of Technology)

时 间： 12月20日（周五） 下午2：00-3：00

地 点： 新数学楼415室

Abstract:
Stochastic particle methods (SPM) for the Boltzmann equation have gained popularity in recent years for the prediction of flows where continuous equations for fluid dynamics are not valid. Among SPMs, the Direct Simulation Monte Carlo (DSMC) methods have been the standard computational method in the field of rarefied gas dynamics. The DSMC method employs a point measure approximation to the distribution function, as simulated particles may possess only a single velocity. This unphysical representation limits the method to converge only weakly to the solution of the Boltzmann equation.

In this talk, we introduce a Distributional Monte Carlo (DMC) method which provides for simulated particles to possess velocity distribution functions, rather than singular velocity vectors. Additionally, we discuss two specific implementations of the technique. The first approach applied kernel density estimation to DSMC. While no variance reduction was observed, the approach was shown to exhibit stronger convergence for the space homogeneous Boltzmann equation. The second implementation represented a hybrid stochastic/deterministic scheme employing the BGK equation for deterministic computation of collision outcomes. When applied to the Bobylev problem, the DMC-BGK method demonstrated a variance reduction of four orders of magnitude over the Nanbu-DSMC method.

报告人简介：
http://www.afit.edu/directory/faclook.cfm?id=300

2. 题 目：Multigrid Methods for Saddle Point Problems

报告人：Li-yeng Sung, Professor
(Department of Mathematics, Louisiana State University)

时 间： 12月20日（周五） 下午3:00-4:00

地 点： 新数学楼415室

Abstract:
We will present multigrid methods for saddle point problems that are uniformly convergent in the energy norms. Examples include saddle point problems arising from mixed finite element discretizations of Stokes, Lam/'e and Darcy systems. This is joint work with Susanne Brenner, Hengguang Li and Duk-Soon Oh.

报告人简介：https://www.math.lsu.edu/~sung/


3. 题 目：C^0 Interior Penalty Methods

报告人：Susanne C. Brenner, Professor
(Department of Mathematics and Center for Computation & Technology, Louisiana State University)

时 间： 12月20日（周五） 下午4:00-5:00

地 点：新数学楼415室

Abstract:
C^0 interior penalty methods are discontinuous Galerkin methods for fourth order problems. In this talk we will discuss the formulation, error analysis and fast solution techniques for these methods. Applications to boundary value problems and variational inequalities will be discussed.

报告人简介：
https://www.math.lsu.edu/~brenner/

欢迎师生们参加！