DMS Graduate Student Seminar

Speaker: Dr. Yimin Zhong 

Title: Fast solver for radiative transfer

Abstract: Constructing efficient numerical solution methods for the equation of radiative transfer (ERT) remains a challenging task in scientific computing despite the tremendous development on the subject in recent years. In this talk, I will present a simple fast computational algorithm for solving the ERT in isotropic media in steady-state and time-dependent settings. The algorithm we developed has two steps. In the first step, we solve a volume integral equation for the angularly-averaged ERT solution using iterative schemes such as the GMRES method. The computation in this step is accelerated with a fast multipole method (FMM). In the second step, we solve a scattering-free transport equation to recover the angular dependence of the ERT solution. The algorithm does not require the underlying medium to be homogeneous. We present numerical simulations under various scenarios to demonstrate the performance of the proposed numerical algorithm for both homogeneous and heterogeneous media. Then I will extend the formulation to anisotropic scattering media and analyze the possibility to apply the fast algorithm.