标题： 单单元反转求解高阶时间依赖辐射传输问题的GPU方法 显示英文标题

标题： One-Cell Inversion for Solving Higher-Order Time-Dependent Radiation Transport on GPUs

摘要： 为了找到瞬态离散 ordinates 中子输运方程的确定性解，通常使用源迭代（SI）来将散射（和裂变）源项从后续迭代中滞后。 对于一维笛卡尔几何，SI 在角度数量上是并行的，但不是在空间单元上；这对于许多核心计算架构（如图形处理单元）是一个缺点。 单单元逆运算（OCI）是一类替代迭代方法，允许在异构计算架构上进行空间并行辐射输运。 对于 OCI，以前的研究表明，在稳态计算中，无论散射比如何，当单元为光学薄时，谱半径趋于1。 在本工作中，我们分析了在用于时间依赖的中子输运计算时，OCI 方案的收敛率如何表现。 我们从简单的角平衡和多重平衡时间离散化方案中推导出一种二阶时空离散化方法，并通过傅里叶分析证明它在时间上是无条件稳定的。 然后，我们推导并数值求解了我们离散化的 OCI 和 SI 分裂的傅里叶系统，结果表明，较小的平均自由时间对 OCI 的谱半径改善比 SI 更明显，并且当平均自由时间变小时，OCI 的谱半径趋于零。 我们将两种求解器扩展为能量相关（使用多群假设）并在 AMD MI250X 上实现，使用供应商提供的批处理 LAPACK 求解器。 更小的时间步长提高了 OCI 相对于 SI 的相对性能，并且即使 OCI 需要更多的迭代次数才能求解一个问题，这些迭代在 GPU 上可以更快地完成。 这导致 OCI 在 GPU 上总体表现优于 SI。 显示英文摘要

摘要： To find deterministic solutions to the transient discrete-ordinates neutron-transport equation, source iterations (SI) are typically used to lag the scattering (and fission) source terms from subsequent iterations. For Cartesian geometries in one dimension, SI is parallel over the number of angles but not spatial cells; this is a disadvantage for many-core compute architectures like graphics processing units. One-cell inversion (OCI) is a class of alternative iterative methods that allow space-parallel radiation transport on heterogeneous compute architectures. For OCI, previous studies have shown that, in steady-state computations, spectral radius tends to unity when cells are optically thin regardless of the scattering ratio. In this work, we analyze how the convergence rate of an OCI scheme behaves when used for time-dependent neutron transport computations. We derive a second-order space-time discretization method from the simple corner balance and multiple balance time discretization schemes and show via Fourier analysis that it is unconditionally stable through time. Then, we derive and numerically solve the Fourier systems for both OCI and SI splittings of our discretization, showing that small mean-free times improve the spectral radius of OCI more than SI, and that spectral radius for OCI tends to zero as mean free time gets smaller. We extend both solvers to be energy dependent (using the multigroup assumption) and implement on an AMD MI250X using vendor-supplied batched LAPACK solvers. Smaller time steps improve the relative performance of OCI over SI, and, even when OCI requires more iterations to converge a problem, those iterations can be done much faster on a GPU. This leads to OCI performing better overall than SI on GPUs.