Structure Preserving Methods for Fokker-Planck-type Equations

报告题目:Structure Preserving Methods for Fokker-Planck-type Equations


报告人:刘海亮教授(Iowa State University






摘要: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.


报告人简介:刘海亮教授1986-1988年在365体育官网app下载应用数学系学习,获理学硕士,后在中科院院系统所继续深造,并获理学博士学位。1997-1999年为德国洪堡访问学者,19992002年在加州大学洛杉矶分校任助理教授。2002年至今在数Iowa State University工作,任副教授、终身教授,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门槛现象及数学理论;(3)保结构的高精度计算方法。自1995年以来,刘海亮教授发表了100余篇研究论文,引用超过1400次。




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