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

Abstract

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.