SIAM Journal on Scientific Computing, Volume 42, Issue 4, Page B869-B893, January 2020.
The discrete ordinates discontinuous Galerkin ($S_N$-DG) method is a well-established and practical approach for solving the radiative transport equation. In this paper, we study a low-memory variation of the upwind $S_N$-DG method. The proposed method uses a smaller finite element space that is constructed by coupling spatial unknowns across collocation angles, thereby yielding an approximation with fewer degrees of freedom than the standard method. Like the original $S_N$-DG method, the low-memory variation still preserves the asymptotic diffusion limit and maintains the characteristic structure needed for mesh sweeping algorithms. While we observe second-order convergence in the scattering dominated, diffusive regime, the low-memory method is in general only first-order accurate. To address this issue, we use upwind reconstruction to recover second-order accuracy. For both methods, numerical procedures based on upwind sweeps are proposed to reduce the system dimension in the underlying Krylov solver strategy.

中文翻译：

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低内存，离散正交，不连续Galerkin方法进行辐射传输

SIAM科学计算杂志，第42卷，第4期，第B869-B893页，2020年1月。
离散坐标不连续伽勒金（$ S_N $ -DG）方法是解决辐射输运方程的公认的实用方法。在本文中，我们研究了逆风$ S_N $ -DG方法的低内存变化。所提出的方法使用较小的有限元空间，该有限元空间是通过在并置角度上耦合空间未知数而构造的，因此与标准方法相比，可以得到具有更少自由度的近似值。像原始的$ S_N $ -DG方法一样，低内存变化仍保留渐近扩散极限并保持网格清扫算法所需的特征结构。虽然我们在以散射为主的扩散模式中观察到了二阶收敛，但低内存方法通常只有一阶精确。为了解决这个问题，我们使用逆风重建来恢复二阶精度。对于这两种方法，都提出了基于迎风扫掠的数值程序，以减小底层Krylov求解器策略中的系统尺寸。