A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation

Abstract

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 $\mathcal{O}$($M$^2+1/$d$) to $\mathcal{O}$($M$^1+1/$d$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.