Title: Multi-scale Simulation for Radiative Transfer Equations

Abstract: Radiative transfer equations are fundamental models to describe the physical phenomena of energy or particle transport through media that are affected by absorption, emission, and scattering processes. The models are mathematically intriguing as they display both transport/hyperbolic properties in the region with weak scattering and diffusive properties where scattering is strong.   Our focus here is on the design and analysis of accurate numerical methods that are uniformly stable for radiative transfer equations in a wide range of regimes. The methods will be presented for a simplified yet relevant model. They start with some reformulations of the equation, and involve high order discontinuous Galerkin methods in space, discrete ordinates methods in the angular direction,  as well as implicit-explicit (IMEX) methods in time with different IMEX strategies. Theoretical findings will be discussed along with a collection of numerical examples.

Bio: Dr. Fengyan Li is a Professor at Rensselaer Polytechnic Institute (RPI). She received her BS and MS degrees in Computational Mathematics from Peking University,  and her PhD degree in Applied Mathematics from Brown University. Dr. Li's research interests are in Numerical Analysis and Scientific Computing, especially in the design and analysis of robust and accurate computational methods for problems arising from areas such as rarefied gas dynamics, plasma physics,  nonlinear optics, and biomedical engineering. Her recent research focuses on multi-scale simulation and reduced order modeling for kinetic transport models (e.g., radiative transfer equations). Dr. Li was a recipient of the Alfred P. Sloan Research Fellowship and the NSF-CAREER award.  She serves on the editorial board of IMA Journal of Numerical Analysis, Mathematics of Computation, SIAM Journal of Numerical Analysis, and CSIAM Transaction on Applied Mathematics. Dr. Li has been actively involved in Association for Women in Mathematics (AWM) and Women in Numerical Analysis and Scientific Computing (WINASC) Research Network.  She was a mentor in the AWM Mentor Network and has been a faculty advisor of the AWM Student Chapter at RPI. Recently, Dr. Li was elected as a 2025 Class of AWM Fellow.