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The multigroup neutron transport equations has been widely used to study theinteractions of neutrons with their background materials in nuclear reactors.High-resolution simulations of the multigroup neutron transport equations usingmodern supercomputers require the development of scalable parallel solvingtechniques. In this paper, we study a scalable transport method for solving thealgebraic system arising from the discretization of the multigroup neutrontransport equations. The proposed transport method consists of a fully coupledNewton solver for the generalized eigenvalue problems and GMRES together with anovel multilevel domain decomposition preconditioner for the Jacobian system.The multilevel preconditioner has been successfully used for many problems, butthe construction of coarse spaces for certain problems, especially forunstructured mesh problems, is expensive and often unscalable. We introduce anew subspace-based coarsening algorithm to address this issue by exploring thestructure of the matrix in the discretized version of the neutron transportproblems. We numerically demonstrate that the proposed transport method ishighly scalable with more than 10,000 processor cores for the 3D C5G7 benchmarkproblem on unstructured meshes with billions of unknowns. Compared with thetraditional multilevel domain decomposition method, the new approach equippedwith the subspace-based coarsening algorithm is much faster on the constructionof coarse spaces.

A scalable multilevel domain decomposition preconditioner with a subspace-based coarsening algorithm for the neutron transport calculations