A space-angle discontinuous Galerkin (saDG) method is used to solve the steady-state radiative transfer equation (RTE) for 2D problems involving absorption, emission, and scattering for a semitransparent medium. This approach discretizes both spatial and angular domains. Parallel computing is based on angular decomposition (AD), and domain decomposition (DD) techniques. The DD technique directly solves the entire domain using the MUMPS library, whereas the AD technique results in an iterative approach for scattering media. This study proposes a novel hybrid AD-DD method, combining the best aspects of both techniques. Numerical results investigate the scalability, performance, and efficiency of AD and DD techniques. It is shown that a hybrid AD-DD technique is superior to these individual techniques by taking advantage of their strengths. Numerical methods demonstrate the applicability of the method of the best combination of hybrid AD-DD to 2D scattering gray media with complex geometries or enclosures with circular and square obstacles.

中文翻译：

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在二维辐射传输中将角度和域分解与空间角间断 Galerkin 方法相结合


空间角间断伽辽金 （saDG） 方法用于求解涉及半透明介质吸收、发射和散射的二维问题的稳态辐射传输方程 （RTE）。这种方法将空间域和角度域离散化。并行计算基于角度分解 （AD） 和域分解 （DD） 技术。DD 技术使用 MUMPS 库直接求解整个域，而 AD 技术则导致散射介质的迭代方法。本研究提出了一种新的混合 AD-DD 方法，结合了两种技术的最佳方面。数值结果研究了 AD 和 DD 技术的可扩展性、性能和效率。结果表明，混合 AD-DD 技术利用它们的优势优于这些单独的技术。数值方法证明了混合 AD-DD 与具有复杂几何形状的 2D 散射灰色介质或具有圆形和方形障碍物的外壳的最佳组合方法的适用性。