TY - JOUR
T1 - A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation
AU - Zhao , Hongkai
AU - Zhong , Yimin
JO - CSIAM Transactions on Applied Mathematics
VL - 2
SP - 346
EP - 364
PY - 2020
DA - 2020/07
SN - 1
DO - http://doi.org/10.4208/csiam-am.2020-0012
UR - https://global-sci.org/intro/article_detail/csiam-am/17182.html
KW - Radiative transport equation, volume integral equation, treecode algorithm.
AB - <p style="text-align: justify;">In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity
from $\mathcal{O}$($M$<sup>2+1/$d$</sup>) to $\mathcal{O}$($M$<sup>1+1/$d$</sup>log$M$), where $M$ is the number of points in the physical
domain. The error analysis is presented and numerical experiments are performed to
validate our algorithm.</p>