论文标题
一种基于扫描的低级别方法，用于离散的纵向传输方程
A sweep-based low-rank method for the discrete ordinate transport equation
论文作者
论文摘要
动力学低级别（DLR）近似是一种有效的技术，可逼近矩阵微分方程的溶液。最近，将DLR方法应用于辐射传输计算，以降低记忆要求和计算成本。这项工作扩展了在2-D和3-D笛卡尔几何形状中具有离散坐标的二-D辐射传输方程的低级方案（SN方法）。通过非常规的基础更新和Galerkin Integrator构建了在低级别歧管上演变的还原系统，以避免及时落后的替代物，这对于耗散问题可能是不稳定的。所得系统通过在角强度具有与方向余弦相同的符号的每个八分位中施加单独的低级别分解来保留在角方向上的信息。然后，运输扫描和源迭代可以有效地解决此低率SN系统。二-D和3-D笛卡尔几何形状的数值结果表明，低级别解决方案所需的记忆和计算时间比使用传输扫描却不丢失准确性而更少。
The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via an unconventional basis update and Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.
