Events
DMS Applied and Computational Mathematics Seminar |
| Time: Feb 14, 2025 (02:00 PM) |
| Location: 328 Parker Hall |
|
Details:  Speaker: Yimin Zhong (Auburn)
Title: Fast solvers for radiative transfer and beyond
Abstract: Despite the tremendous developments in recent years, constructing efficient numerical solution methods for the radiative transfer equation (RTE) is still challenging in scientific computing. In this talk, I will present a simple yet fast computational algorithm for solving the RTE 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 solution using iterative schemes such as the GMRES method. The computation in this step is accelerated with a variant of the fast multipole method (FMM). In the second step, we solve a scattering-free transport equation to recover the angular dependence of the 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 the time-domain and anisotropic scattering media and analyze the possibility of applying the fast algorithm.
|