Massively Parallel Transport Sweeps on Meshes with Cyclic Dependencies

Abstract: 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.