Colloquium: Dr. Li Wang, Department of Mathematics, UCLA

Dr. Li Wang, Department of Mathematics, UCLA

Title: Asymptotic-Preserving schemes for multi-scale semiconductor Boltzmann equation 

Abstract: Kinetic equations often contain multiple scales that lead to various asymptotic regimes, in which classical numerical methods become prohibitively expensive. Asymptotic-Preserving (AP) scheme is one efficient way to treat such multiscale problems. It is a unified kinetic solver that automatically solves the macroscopic equations in the small scale regime by preserving the asymptotic limit at the discrete level. In this talk, I will present AP schemes for the semiconductor Boltzmann equation in a diffusive scaling with two-scale collisions that leads to an energy-transport system for electron mass and internal energy as mean free path goes to zero. Our scheme is based on a BGK (Bhatnagar-Gross-Krook) penalization together with a spatially dependent threshold on the stiffer collision operator such that the evolution of the solution resembles a Hilbert expansion at the continuous level. An alternative approach via a splitting strategy will also be presented which can systematically treat the collisions at different scales separately. Formal asymptotic analysis and numerical results confirm the efficiency and accuracy of the schemes. In the end, I will illustrate the promise of these ideas in treating the hierarchy of macroscopic models in semiconductors and other applications.

 
Faculty host: Yanzhao Cao