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The multigroup neutron transport equations have been widely used to study themotion of neutrons and their interactions with the background materials.Numerical simulation of the multigroup neutron transport equations iscomputationally challenging because the equations is defined on a highdimensional phase space (1D in energy, 2D in angle, and 3D in spatial space),and furthermore, for realistic applications, the computational spatial domainis complex and the materials are heterogeneous. The multilevel domaindecomposition methods is one of the most popular algorithms for solving themultigroup neutron transport equations, but the construction of coarse spacesis expensive and often not strongly scalable when the number of processor coresis large. In this paper, we study a highly parallel multilevelNewton-Krylov-Schwarz method equipped with several novel components, such assubspace-based coarsening, partition-based balancing and hierarchical meshpartitioning, that enable the overall simulation strongly scalable in terms ofthe compute time. Compared with the traditional coarsening method, thesubspace-based coarsening algorithm significantly reduces the cost of thepreconditioner setup that is often unscalable. In addition, the partition-basedbalancing strategy enhances the parallel efficiency of the overall solver byassigning a nearly-equal amount of work to each processor core. Thehierarchical mesh partitioning is able to generate a large number of subdomainsand meanwhile minimizes the off-node communication. We numerically show thatthe proposed algorithm is scalable with more than 10,000 processor cores for arealistic application with a few billions unknowns on 3D unstructured meshes.

A highly parallel multilevel Newton-Krylov-Schwarz method with  subspace-based coarsening and partition-based balancing for the multigroup  neutron transport equations on 3D unstructured meshes