A fast algorithm for radiative transport in isotropic media

• Published in: Journal of computational physics Vol. 399; p. 108958
• Main Authors: Ren, Kui, Zhang, Rongting, Zhong, Yimin
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 15.12.2019; Elsevier Science Ltd
• Subjects: Algorithms; Computational physics; Computer simulation; Dependence; Diffusion approximation; Equation of radiative transfer; Fast algorithm; Isotropic media; Iterative methods; Kernel-independent fast multipole method; Low-rank approximation; Multipoles; Numerical analysis; Numerical methods; Radiative transfer; Transport equations; Volume integral equation; Volume integral equations; Diffusion approximation; Kernel-independent fast multipole method; Low-rank approximation; Fast algorithm; Equation of radiative transfer; Volume integral equation
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2019.108958

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.