When solving the first-order form of the linear Boltzmann equation, a common misconception is that the matrix-free computational method of “sweeping the mesh”, used in conjunction with the Discrete Ordinates method, is too complex or does not scale well enough to be implemented in modern high performance computing codes. This has led to considerable efforts in the development of matrix-based methods that are computationally expensive and is partly driven by the requirements placed on modern spatial discretizations. In particular, modern transport codes are required to support higher order elements, a concept that invariably adds a lot of complexity to sweeps because of the introduction of cyclic dependencies with curved mesh cells. In this article we will present a comprehensive implementation of sweeping, to a piecewise-linear DFEM spatial discretization with particular focus on handling cyclic dependencies and possible extensions to higher order spatial discretizations. These methods are implemented in a new C++ simulation framework called Chi-Tech ($\chi -Tech$). We present some typical simulation results with some performance aspects that one can expect during real world simulations, we also present a scaling study to >100k processes where Chi-Tech maintains greater than 80% efficiency solving a total of 87.7 trillion angular flux unknowns for a 116 group simulation.

在求解线性Boltzmann方程的一阶形式时，一个常见的误解是与离散Ordinates方法结合使用的“无网格扫描”的无矩阵计算方法过于复杂或无法很好地缩放以至于用现代高性能计算代码实现。这导致了开发基于矩阵的方法的大量工作，这些方法在计算上是昂贵的，部分原因是对现代空间离散化提出了要求。特别是，现代运输代码需要支持更高阶的元素，由于引入了带有弯曲网格单元的循环依赖性，这一概念总是会增加扫描的复杂性。在本文中，我们将介绍清除的全面实现，分段线性DFEM空间离散化，特别着重于处理循环依赖性和可能的​​扩展到更高阶空间离散化。这些方法是在称为Chi-Tech（$\chi -ŤËCH$）。我们提供了一些典型的仿真结果，以及一些在实际仿真中可以预期的性能方面，我们还提供了对超过100k流程的缩放研究，其中Chi-Tech保持了80％以上的效率，解决了87.7万亿个角通量未知数116组模拟。