# A low-rank Schwarz method for radiative transport equation with heterogeneous scattering coefficient

## TL;DR

This paper introduces an accelerated Schwarz method leveraging random sampling to efficiently solve multiscale radiative transfer equations with heterogeneous scattering coefficients, demonstrating high accuracy and robustness.

## Contribution

The work develops a novel low-rank Schwarz method using offline random sampling for local solution maps, improving efficiency in multiscale radiative transfer problems.

## Key findings

- Method achieves high accuracy in numerical tests
- Approach is robust across different heterogeneity levels
- Significant reduction in computational cost

## Abstract

Random sampling has been used to find low-rank structure and to build fast direct solvers for multiscale partial differential equations of various types. In this work, we design an accelerated Schwarz method for radiative transfer equations that makes use of approximate local solution maps constructed offline via a random sampling strategy. Numerical examples demonstrate the accuracy, robustness, and efficiency of the proposed approach.