Structure Preserving Methods for Fokker-Planck-type Equations
主 题: Structure Preserving Methods for Fokker-Planck-type Equations
报告人: Professor Hailiang Liu (Iowa State University)
时 间: 2014-10-29 14:00-15:00
地 点: 数学中心甲乙丙楼82J04（数学中心计算方法与应用实验室双周讨论班学术报告、北京计算数学学会系列报告）
Kinetic Fokker-Planck equations arise in many applications, and thus there has been considerable interest in the development of accurate numerical methods to solve them. The peculiar feature of these models is that the transient solution converges to certain equilibrium when time becomes large. For the numerical method to capture the long-time pattern of the underlying solution, some structure preserving methods have been designed to preserve physical properties exactly at the discrete level. I shall explain the main ideas and challenges through several examples, including the Fokker-Planck equation of the dumbbell model for polymers, a reaction-diffusion-advection equation for the evolution of biased dispersal of population dynamics, and a direct competitive selection model. Numerical results are reported to illustrate the capacity of the proposed algorithms
刘海亮教授1986-1988年在清华大学应用数学系学系，获理学硕士，后在中科院院系统科学所继续深造，并获理学博士学位。1997-1999年为德国洪堡访问学者，1999－2002年在加州大学洛杉机分校任助理教授。2002年至今在Iowa State University工作，任数学教授，和应用数学首席(Holl Chair).
刘海亮教授多年来致力于发展新的数学工具和计算方法求解某些重要应用中出现的发展型偏微分方程,近几年的工作和成果主要集中在以下几个方面: (1)渐近分析和数值建模; (2)应用偏微分方程中临界现象及数学理论;(3)保结构的高精度计算方法. 自1992年以来，刘海亮教授发表了100余篇研究论文，引用超过1400次。
