报告题目：Some computational methods for kinetic transport equations

报告人：程颖达 教授 弗吉尼亚理工大学(Virginia tech)

报告时间：12月15日  10:00-11:00

报告地点：管理楼1418

摘要：Kinetic equations are mesoscale description of the transport of particles such as neutrons, photons, electrons, molecules as well as their interaction with a background medium or among themselves, and they have wide applications in many areas of mathematical physics, such as nuclear engineering, fusion device, optical tomography, rarefied gas dynamics, semiconductor device design, traffic network, swarming, etc. Because the equations are posed in the phase space (physical space plus velocity space), any grid based method will run into computational bottleneck in real applications that are 3D in physical space and 3D in velocity space. This talk will present three numerical solvers that we developed aiming at efficient computations of kinetic equations: the adaptive sparse grid discontinuous Galerkin method, the reduced basis method and the machine learning moment closure method. They aim at effective reduced order computations of such high dimensional equations. Benchmark numerical examples will be presented.

个人简介： 

程颖达教授任职于数学系和CMDA (computational modeling and data anytics) program。程教授曾获得NSF CAREER Award和Simons Fellow。程教授于2023年获得SIAM 美国工业应用数学学会Germund Dhalquist Prize,是本奖项第一个中国获奖人。研究方向包括数值分析、科学计算、偏微分方程数值解以及数据驱动的建模和计算。