Quasi-Monte Carlo Radiative Transfer

TL;DR

This paper explores the use of Quasi-Monte Carlo methods as an efficient alternative to traditional Monte Carlo simulations for dust radiative transfer, demonstrating significantly improved convergence and computational speed.

Contribution

It introduces Quasi-Monte Carlo techniques to radiative transfer simulations and compares their performance with Monte Carlo methods across various geometries and problems.

Findings

Quasi-Monte Carlo converges faster than Monte Carlo.

Achieved up to 40 times faster computation for fixed error.

Observed at least 10 times speed-up in multiple test cases.

Abstract

We consider an alternative to the Monte Carlo method for dust continuous radiative transfer simulations: the Quasi-Monte Carlo method. We briefly discuss what it is, its history, and possible implementations. We compare the Monte Carlo method with four pseudo-random number generators and five Quasi-Monte Carlo implementations using different low-discrepancy sequences and the Hammersley set. For the comparison, we study different test matter geometries and problems. We present comparison results for single scatterings of radiation from a point source, multiple scatterings of radiation from a point source, and single scatterings of radiation from a spherical star. In all cases, Quasi-Monte Carlo shows better convergence than Monte Carlo. In several test cases, the gain in computation time to achieve a fixed error value reached 40 times. We obtained ten times speed up in many of the considered tests.