报告题目：Fourier spectral method for the Boltzmann equation

报告时间：2025年6月26日下午16:20-17:20

报告地点：龙洞行政楼610报告厅

报 告 人：蔡振宁副教授（新加坡国立大学）

邀 请 人：况阳

报告摘要: The Boltzmann equation is a cornerstone of gas kinetic theory, describing the statistical behavior of gas molecules via distribution functions. Its high dimensionality and the complex structure of the collision operator make numerical solutions particularly challenging. In this talk, we will explore how the Fourier spectral method enhances the efficiency of numerical solvers for the Boltzmann equation. Based on a review of the development of Fourier spectral methods, we will show our improvement of Fourier spectral methods by fixes of conservation laws, entropy dissipation and the positivity of distribution functions. Additionally, we will introduce a modified Newton's method for the steady-state Boltzmann equation based on a fast Fourier spectral method to evaluate the linearized collision term, which can significantly accelerate the iteration towards the steady state.

报告人介绍：Zhenning CAI is currently an associate professor at Department of Mathematics, National University of Singapore. He obtained his PhD degree in 2013 from Peking University, China, after which he was funded by Humboldt foundation in Germany and worked as a postdoctoral researcher from 2014 to 2015. In 2016, he moved firstly to University of Maryland and then to Duke University in USA. He joined National University of Singapore as an assistant professor in 2017 and was promoted to associate professor in 2023. His research work focuses mainly on the modeling and simulation of gas kinetic theories and numerical methods for open quantum systems.