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<p>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 solving the steady-state RTE in heterogeneous media, which can adaptively compress the angular space. It does so by selecting reduced TFPS basis functions, guided by prior knowledge of the local optical properties of the background media. These reduced basis functions capture the important local modes in the angular space, which are then pieced together by ensuring the continuity of angular flux in these important angular modes. A detailed a posteriori error analysis is performed to quantify the discrepancy between the reduced TFPS solution with adaptive angular compression and the full TFPS solution. Additionally, numerical experiments demonstrate the efficiency and accuracy of the Adaptive TFPS in solving multiscale RTEs, especially in scenarios involving boundary and interface layers.</p>

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

  • 期刊论文

  • 发表日期：

    2025年6月21日

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  • Qinchen Song,
  • Jingyi Fu,
  • Min Tang,
  • Lei Zhang

摘要

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 solving the steady-state RTE in heterogeneous media, which can adaptively compress the angular space. It does so by selecting reduced TFPS basis functions, guided by prior knowledge of the local optical properties of the background media. These reduced basis functions capture the important local modes in the angular space, which are then pieced together by ensuring the continuity of angular flux in these important angular modes. A detailed a posteriori error analysis is performed to quantify the discrepancy between the reduced TFPS solution with adaptive angular compression and the full TFPS solution. Additionally, numerical experiments demonstrate the efficiency and accuracy of the Adaptive TFPS in solving multiscale RTEs, especially in scenarios involving boundary and interface layers.