应数学系计算数学研究所邀请，美国伦斯勒理工学院李凤艳博士将于近期访问公司，报告信息如下，欢迎感兴趣的老师和同学参加。

报告题目：Advances in high order methods for some kinetic models

地点：格物楼503

时间：2014年12月22日上午 10：30-11:30

报告摘要: 

         In this talk, I will present our recent work in developing high order methods to simulate some kinetic models.

         We first start with the VlasovMaxwell system which is an important model for collisionless magnetized plasmas. The focus is particularly on the evolution of single-species particles, electrons, under the self-consistent electromagnetic field while the ions are regarded as the fixed background. For this model, we formulate discontinuous Galerkin (DG) methods in phase space. These semi-discrete methods can be designed as accurate as one wants, while with provable conservation of mass and possibly total energy. Such properties are often hard to achieve within many other numerical method frameworks. Error estimates are established for several flux choices, and also when a third order Runge-Kutta method is applied in time. The algorithms are tested on the streaming Weibel instability in terms of accuracy, conservation, and robustness.

        We then move to some kinetic models in a diffusive scaling, with examples including the telegraph equation, the porous medium model, and the one-group transport equation in slab geometry. For these models, high order asymptotic preserving methods are developed, which are based on three ingredients: micro-macro decomposition, DG spatial discretization, and globally stiffly accurate implicit-explicit Runge-Kutta temporal discretizations. Uniform stability is further obtained with respect to the Knudsen number epsilon, along with the error estimates as well as rigorous asymptotic analysis when epsilon goes to zero.

报告人简介

         Rensselaer Polytechnic Institute 副教授。1997年和2000年在北京大学分别获得计算数学学士和硕士学位。2004年在美国布朗大学获得应用数学博士学位。2004年至2006年在美国南卡莱罗纳大学数学系任博士后。2006年至今任职于Rensselaer Polytechnic Institute的数学科学系。2008年当选为Alfred P. Sloan Research Fellow，2009年获美国NSF-CAREER 奖。现任 SIAM Journal on Scientific Computing 副主编。主要的科研兴趣和领域是高精度算法的设计，分析和计算。 涉及到的应用领域包括电磁学，计算流体学，天体物理，等离子物理，和动力学方程等。