Abstract: The Boltzmann equation is a cornerstone of gas kinetic theory, describing the statistical behavior of gas molecules via distribution functions. However, its high dimensionality and the complex, nonlinear structure of the collision operator present significant challenges for numerical computation. Over the past decade, our research has focused on both model reduction and efficient numerical methods for solving the Boltzmann equation. In this talk, I will highlight recent progress on the simplification and acceleration of algorithms for the quadratic collision operator. In particular, I will present two classes of spectral methods–one based on Hermite polynomials and the other on Fourier basis functions–that effectively reduce computational cost while maintaining accuracy.

Bio: Zhenning Cai received his Ph.D. from Peking University in 2013. He then conducted postdoctoral research at RWTH Aachen University for two years, followed by a one-year appointment as a Visiting Assistant Professor at Duke University. In 2017, he joined the Department of Mathematics at the National University of Singapore, where he was promoted to Associate Professor with tenure in 2023. His research interests lie primarily in the modeling and simulation of rarefied gas dynamics and the numerical computation of open quantum systems.