A fast algorithm for radiative transport in isotropic media

JOURNAL OF COMPUTATIONAL PHYSICS

卷:399

Article

Ren, Kui^1,2  Zhang, Rongting¹  Zhong, Yimin¹ 

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Texas Austin, Oden Inst, Austin, TX 78712 USA

关键词: Fast algorithm;    Equation of radiative transfer;    Volume integral equation;    Kernel-independent fast multipole method;    Low-rank approximation;    Diffusion approximation;   

DOI  :  10.1016/j.jcp.2019.108958

来源: Elsevier

【 摘 要 】

Constructing efficient numerical solution methods for the equation of radiative transfer (ERT) remains as a challenging task in scientific computing despite of the tremendous development on the subject in recent years. We present in this work a simple fast computational algorithm for solving the ERT in isotropic media. 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 be homogeneous. We present numerical simulations under various scenarios to demonstrate the performance of the proposed numerical algorithm for both homogeneous and heterogeneous media. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free