An Adaptive Angular Domain Compression Scheme For Solving Multiscale Radiative Transfer Equation

TL;DR

This paper presents an adaptive angular compression scheme for multiscale radiative transfer equations, improving computational efficiency by locally tailoring basis functions based on media properties.

Contribution

It introduces an adaptive finite point scheme that compresses angular space using local optical property-based basis functions, with rigorous error analysis and numerical validation.

Findings

Efficiently captures local angular modes in heterogeneous media.

Achieves accurate solutions with reduced computational cost.

Demonstrates effectiveness in boundary and interface layer scenarios.

Abstract

When dealing with the steady-state multiscale radiative transfer equation (RTE) with heterogeneous coefficients, spatially localized low-rank structures are present in the angular space. This paper introduces an adaptive tailored finite point scheme (TFPS) for RTEs in heterogeneous media, which can adaptively compress the angular space. It does so by selecting reduced TFPS basis functions based on the local optical properties of the background media. These reduced basis functions capture the important local modes in the velocity domain. A detailed a posteriori error analysis is performed to quantify the discrepancy between the reduced and full TFPS solutions. Additionally, numerical experiments demonstrate the efficiency and accuracy of the adaptive TFPS in solving multiscale RTEs, especially in scenarios involving boundary and interface layers.