The Quantization Monte Carlo method for solving radiative transport equations

TL;DR

The paper presents the Quantization Monte Carlo method, a novel approach for efficiently solving thermal radiative transport equations across multiple collision regimes by precomputing escape distributions and sampling from quantized data.

Contribution

It introduces a new Monte Carlo technique that replaces multiple collisions with precomputed escape distributions, enabling efficient simulation across different collision regimes.

Findings

Method performs well on benchmark tests

Escape laws depend smoothly on parameters

Efficient sampling from precomputed distributions

Abstract

We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given simulation cell, the proposed method advances the time by replacing many collisions with sampling directly from the escape distribution of the particle. In order to perform the sampling, for each triplet of parameters (opacity, remaining time, initial position in the cell) on a parameter grid, the escape distribution is precomputed offline and only the quantiles are retained. The online computation samples only from this quantized (i.e., discrete) version by choosing a parameter triplet on the grid (close to actual particle's parameters) and returning at random one quantile from the precomputed set of quantiles for that parameter. We first check numerically that the escape laws depend smoothly on the parameters and then implement the procedure on a benchmark with good results.