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 timedependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity from O(M 2+1/d) to 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.