In this talk, we consider a linear kinetic transport equation under a diffusive scaling, that has a diffusive equation as the limit when the Knudsen number goes to zero. The equation provides a prototype model to study many systems, including neutronic dynamics and radiation transfer. One type of numerical methods that can simulate such multi-scale models efficiently is the asymptotic preserving (AP) method. Our focus here is on devising accurate AP methods, that are uniformly stable from transport to diffusive regimes, by applying discontinuous Galerkin (DG) methods in space and implicit-explicit (IMEX) Runge-Kutta methods in time. We will present several families of IMEX-DG methods based on  different reformulations of the model and different IMEX strategies. Computational complexity and theoretical findings will be discussed, along with some numerical examples.

Dr. Fengyan Li is a professor in the Department of Mathematical Sciences at Rensselaer Polytechnic Institute (RPI). Before joining RPI in 2006, she held a postdoc position at University of South Carolina. She received her BS and MS degrees in Computational Mathematics from Peking University in 1997 and 2000, respectively, and her PhD degree in Applied Mathematics from Brown University in 2004.  Dr. Li received an Alfred P. Sloan Research Fellowship in 2008, and an NSF-CAREER award in 2009. Her research interests mainly lie in the design, analysis, implementation and applications of high order and structure-preserving numerical methods for electromagnetism, magnetohydrodynamics, Hamilton–Jacobi equations and various kinetic models.