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The multigroup neutron transport criticality calculations using modernsupercomputers have been widely employed in a nuclear reactor analysis forstudying whether or not a system is self-sustaining. However, the design anddevelopment of efficient parallel algorithms for the transport criticalitycalculations is challenging especially when the number of processor cores islarge and an unstructured mesh is adopted. In particular, both the compute timeand memory usage have to be carefully taken into consideration due to thedimensionality of the neutron transport equations. In this paper, we study amonolithic multilevel Schwarz preconditioner for the transport criticalitycalculations based on a nonlinear diffusion acceleration (NDA) method. Wepropose a monolithic multilevel Schwarz method that is capable of efficientlyhandling the systems of linear equations for both the transport system and thediffusion system. However, in the multilevel method, algebraically constructingcoarse spaces is expensive and often unscalable. We study a subspace-basedcoarsening algorithm to address such a challenge by exploring the matrixstructures of the transport equations and the nonlinear diffusion equations. Wenumerically demonstrate that the monolithic multilevel preconditioner with thesubspace-based coarsening algorithm is twice as fast as that equipped with anunmodified coarsening approach on thousands of processor cores for anunstructured mesh neutron transport problem with billions of unknowns.

Neutron transport criticality calculations using a parallel monolithic  multilevel Schwarz preconditioner together with a nonlinear diffusion  acceleration method