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 formula-tion 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.

Keywords

Radiative transport equation / volume integral equation / treecode algorithm